Abstract: To solve the ill-posed pr oblem of spectral unmixing in hyperspectral subpixel mapping applications, the maximum a posteriori estimation (MAP) spectral unmixing model combined with spatial distribution prior total variation (TV) was improved to ensure the scalability of the algorithm and the uniqueness of the solution. At the same time, in order to solve the cumbersome problem caused by the inherent nonlinear characteristics of TV prior, a fast algorithm was proposed to transform the original complex nonlinear operation into several simple operations with closed solutions. To solve the sub-problem respectively, a fast iterative shrinkage threshold algorithm (FISTA) and the split Bregman algorithm were utilized. The results show that the proposed new method can maintain the consistent mapping accuracy of the traditional gradient descent method, and can increase the iteration speed by more than 10 times, providing higher computational efficiency.