JSFiddle - React, Tailwind, and code Playground

JavaScript

var array = ["1-jun-15", "1-feb-15", "1-apr-15", "1-may-15", "1-jan-15", "1-mar-15"];

var sorted = array.sort(function(a, b) {
  return new Date(a).getTime() - new Date(b).getTime();
});

console.log(array);