Let f (z) be a meromorphic functions with finite order , R(z) be a nonconstant rational function and k be a positive integer. In this paper, we consider the difference equation originated from Schwarzian differential equation, which is of form ∆ 3 f (z)∆ f (z) − 3 2 (∆ 2 f (z)) 2 k = R(z)(∆ f (z)) 2k. We investigate the uniqueness of meromorphic solution f of difference Schwarzian equation if f shares three values with any meromrphic function. The exact forms of meromorphic solutions f of difference Schwarzian equation are also presented.