Up to now, it is a hard work to find the corresponding information criterions for minor generalized components in many signal processing fields, and only one dimension minor generalized component can be extralted. In order to solve this problem, this paper proposes a multiple minor generalized components extraction information criterion, which is proved to have only one global maximum. A novel algorithm is also derived by using gradient ascent method to this information criterion. The global convergence of the proposed algorithm is analyzed by using the Lyapunov function method. Compared with existing algorithms, the proposed algorithm does not need normalization operation and can extract multiple minor generalized components in parallel. Simulation results show the accuracy and the speed advantages of the proposed algorithm.