Hei, is there possible to take faster train from Changsha to Zhangjiajie?

There are only several normal-speed trains that operate between these two cities.
The trains from Changsha Railway Station depart at 03:49, 05:47, 07:44, 11:39, 20:30 and 22:39. It takes around 5 to 6 hours. The ticket fare of soft sleeper is about CNY161.5, hard sleeper is about CNY108.5 and hard seat is about CNY54.5.

May I know how you purchase the train tickets in advance? I am interested in the 3.00+ a.m train to ZJJ. I reach Changsha by flight at 11.00+ p.m.

You can book the ticket through TravelChinaGuide. They provide online train ticket booking service. Their contact information is bookingtravelchinaguide.com. :)