Here is the brute force method:
var time = "20150605-16:34:53.506";
var year = parseInt(time.substr(0, 4), 10);
var month = parseInt(time.substr(4, 2), 10) - 1;
var day = parseInt(time.substr(6, 2), 10);
var hour = parseInt(time.substr(9, 2), 10);
var minute = parseInt(time.substr(12, 2), 10);
var second = parseInt(time.substr(15, 2), 10);
var mille = parseInt(time.substr(18, 3), 10);
var date = new Date(year, month, day, hour, minute, second, mille);
console.log(date);
> Fri Jun 05 2015 16:34:53 GMT-0700 (PDT)
See MDN Date for more details. Note that month is odd -- it is zero-based unlike year and day (thus the -1 on the parsed month):
month
Integer value representing the month, beginning with 0 for January to 11 for December.