尝试这样：

func indexOfCharacter(myString:String, char: Character,fromIndex: Int) -> Int {

    let sub = myString.substringFromIndex(advance(myString.startIndex, fromIndex))
    if let idx = find(sub, char) {
        return distance(sub.startIndex, idx) + fromIndex
    }else{
        return -1
    }

}

let myString = "abcdabcd"

indexOfCharacter(myString, "d", 4)   // 7

更新： Xcode 7.3•Swift 2.2

func indexOfCharacter(myString:String, char: Character, fromIndex: Int) -> Int {

    let sub = myString.substringFromIndex(myString.startIndex.advancedBy(fromIndex))
    if let idx = sub.characters.indexOf(char){
        return sub.startIndex.distanceTo(idx) + fromIndex
    }else{
        return -1
    }

}