Swift 4.x 版本

    let path = NSSearchPathForDirectoriesInDomains(.documentDirectory, .userDomainMask, true)[0] as String
    let url = NSURL(fileURLWithPath: path)
    if let pathComponent = url.appendingPathComponent("nameOfFileHere") {
        let filePath = pathComponent.path
        let fileManager = FileManager.default
        if fileManager.fileExists(atPath: filePath) {
            print("FILE AVAILABLE")
        } else {
            print("FILE NOT AVAILABLE")
        }
    } else {
        print("FILE PATH NOT AVAILABLE")
    }

Swift 3.x 版本

    let path = NSSearchPathForDirectoriesInDomains(.documentDirectory, .userDomainMask, true)[0] as String
    let url = URL(fileURLWithPath: path)

    let filePath = url.appendingPathComponent("nameOfFileHere").path
    let fileManager = FileManager.default
    if fileManager.fileExists(atPath: filePath) {
        print("FILE AVAILABLE")
    } else {
        print("FILE NOT AVAILABLE")
    }

Swift 2.x 版本，需要使用 URLByAppendingPathComponent

    let path = NSSearchPathForDirectoriesInDomains(.DocumentDirectory, .UserDomainMask, true)[0] as String
    let url = NSURL(fileURLWithPath: path)
    let filePath = url.URLByAppendingPathComponent("nameOfFileHere").path!
    let fileManager = NSFileManager.defaultManager()
    if fileManager.fileExistsAtPath(filePath) {
        print("FILE AVAILABLE")
    } else {
        print("FILE NOT AVAILABLE")
    }