更新：Xcode 8.3.2 · Swift 3.1
问题是你总是一遍又一遍地得到相同的位置。试试这样：

import UIKit
import MapKit

class ViewController: UIViewController,  CLLocationManagerDelegate {
    @IBOutlet weak var mapView: MKMapView!
    let locationManager = CLLocationManager()
    var startLocation: CLLocation!
    var lastLocation: CLLocation!
    var startDate: Date!
    var traveledDistance: Double = 0
    override func viewDidLoad() {
        super.viewDidLoad()
        if CLLocationManager.locationServicesEnabled() {
            locationManager.delegate = self
            locationManager.desiredAccuracy = kCLLocationAccuracyBest
            locationManager.requestWhenInUseAuthorization()
            locationManager.startUpdatingLocation()
            locationManager.startMonitoringSignificantLocationChanges()
            locationManager.distanceFilter = 10
            mapView.showsUserLocation = true
            mapView.userTrackingMode = .follow
        }
    }
    func locationManager(_ manager: CLLocationManager, didUpdateLocations locations: [CLLocation]) {
        if startDate == nil {
            startDate = Date()
        } else {
            print("elapsedTime:", String(format: "%.0fs", Date().timeIntervalSince(startDate)))
        }
        if startLocation == nil {
            startLocation = locations.first
        } else if let location = locations.last {
            traveledDistance += lastLocation.distance(from: location)
            print("Traveled Distance:",  traveledDistance)
            print("Straight Distance:", startLocation.distance(from: locations.last!))
        }
        lastLocation = locations.last
    }
    func locationManager(_ manager: CLLocationManager, didFailWithError error: Error) {
        if (error as? CLError)?.code == .denied {
            manager.stopUpdatingLocation()
            manager.stopMonitoringSignificantLocationChanges()
        }
    }
}

Sample Project

如果您要计算两点之间的路径距离，则需要使用MKDirectionsRequest，这将返回一条或多条从A点到B点的路径，其中包含分步说明：

class func caculateDistance(){
    var directionRequest = MKDirectionsRequest()
    var sourceCoord = CLLocationCoordinate2D(latitude: -36.7346287, longitude: 174.6991812)
    var destinationCoord = CLLocationCoordinate2D(latitude: -36.850587, longitude: 174.7391745)
    var mkPlacemarkOrigen = MKPlacemark(coordinate: sourceCoord, addressDictionary: nil)
    var mkPlacemarkDestination = MKPlacemark(coordinate: destinationCoord, addressDictionary: nil)
    var source:MKMapItem = MKMapItem(placemark: mkPlacemarkOrigen)
    var destination:MKMapItem = MKMapItem(placemark: mkPlacemarkDestination)
    directionRequest.setSource(source)
    directionRequest.setDestination(destination)
    var directions = MKDirections(request: directionRequest)
    directions.calculateDirectionsWithCompletionHandler {
        (response, error) -> Void in
        if error != nil { println("Error calculating direction - \(error.localizedDescription)") }
        else {
            for route in response.routes{
                println("Distance = \(route.distance)")
                for step in route.steps!{
                    println(step.instructions)
                }  
            }
        }
    }
}

此示例代码将返回以下内容：

Distance
Distance = 16800.0

Step by Step instructions
Start on the route
At the end of the road, turn left onto Bush Road
Turn right onto Albany Expressway
At the roundabout, take the first exit onto Greville Road toward 1, Auckland
At the roundabout, take the third exit to merge onto 1 toward Auckland
Keep left
Take exit 423 onto Shelly Beach Road
Continue onto Shelly Beach Road
At the end of the road, turn right onto Jervois Road
Turn left onto Islington Street
Keep right on Islington Street
Arrive at the destination

该函数可以很容易地修改为接收两个位置并返回距离和任何其他所需的信息。
希望对你有帮助！

Leo Dabus方法可用于计算您的实际位置与开始位置之间的地理距离。
为了获得精确的行驶距离，您必须使用最后一个位置和旧位置之间的差异来更新“traveledDistance”。
这是我的实现：

var startLocation:CLLocation!
var lastLocation: CLLocation!
var traveledDistance:Double = 0

func locationManager(manager: CLLocationManager!, didUpdateLocations locations: [AnyObject]!) {
    if startLocation == nil {
        startLocation = locations.first as! CLLocation
    } else {
        let lastLocation = locations.last as! CLLocation
        let distance = startLocation.distanceFromLocation(lastLocation)
        startLocation = lastLocation
        traveledDistance += distance 
    }
}