I am working on dinamic web site it works fine with History API but I heard about some browsers issue about it.Which browsers support it?Then I decided to use history.js but it contains eval function and I know it is dangerous and slow.Shoul I use history.js or how?
Unless you need to worry about supporting IE8 or earlier, or Opera Mini (at all) you should be fine with just the History API. Please see http://caniuse.com/#feat=history for more information.
In general, if you want to know if it's OK to use any browser APIs you'll find the answer on http://caniuse.com.