Abstract: Variable-coefficients nonlinear evolution equations offer us with more real aspects in the inhomogeneities of media and non-uniformities of boundaries than their counter constant-coefficients in some real-world problems, so it is of great significance to study the nonlinear evolution equation with variable coefficients. Firstly the (2+1) dimensional nonlinear chiral Schrödinger equation with variable coefficients is transformed into an ordinary differential equation by the fractional complex transformation. Then, the real part and imaginary part are separated and set to zero respectively. By using the G^'/G²- expansion method, a series of general exact traveling wave solutions with parameters are obtained, which include rational function solutions, trigonometric function solutions and hyperbolic function solutions. Finally, when the parameter takes a special value, the kink wave solution, periodic wave solution and solitary wave solution are worked out in turn.