Exact hyperbolic, trigonometric and rational travelling wave solutions to the (2+ 1)-dimensional Generalized Zakharov-Kuznetsov (GZK) equation via the extended generalized Riccati equation mapping method are presented in this paper. The twenty one travelling wave solutions obtained were verified by putting them back into the GZK equation with the aid of Mathematica. This shows that the extended generalized Riccati equation mapping method is a powerful tool for finding exact solution to nonlinear partial differential equations in physics, mathematics and other applications.