Amplitude variation with angle (AVA) inversion is one of the most effective techniques in hydrocarbon exploration and estimating subsurface petrophysical properties. The inversion problem as a nonlinear, multiparameter, and multimodal optimization problem is conventionally solved through linearized optimization methods, but with the cost of smoothing important geologic interfaces. In addition, the results obtained by these methods are more possible to be trapped in a local minimum, while global-optimization methods can produce more accurate results and preserve the interfaces of geologic structures. A Bayesian framework is used to formulate the AVA inversion problem, which incorporates a novel prior constraint included by two regularization functions, one for sparsity of the coefficients as well as recovering discontinuities and another one for enhancing the lateral continuity. The imperialist competitive algorithm as an efficient evolutionary algorithm is then used to optimize the resulted objective function, to invert the P-and S-wave velocities as well as the density. We compare our algorithm with a commonly used Bayesian linearized inversion method by applying both methods on synthetic data and real seismic data from Gulf of Mexico. Our results reveal the practicability and stability of the presented method for the AVA inversion problem.