By extending the square map，a one-dimensional generalized square map with exponential term is constructed，and its corresponding two-dimensional map is obtained via one-order coupled item in this paper. By using the one-parameter bifurcation diagram，two-parameter dynamics behavior distribution diagram，iterative mapping curve and attractor phase graphics，these generalized square maps are analyzed and simulated. The research results indicate that one-dimensional generalized square map distributes in the unit region and has the nonlinear dynamical phenomenon similar to single-peak square map，and two-dimensional generalized square map has the phenomenon of Hopf bifurcation and locked-frequency shown with complex，flexible and strange-shaped limit cycles and chaotic attractors.