A fast self-adaptive differential evolution algorithm(FSADE) for the complex nonlinear power economic load dispatch problem is proposed. In the view of vector operation, the mutant operator of basic differential evolution algorithm is analyzed, then an improved mutant operator is proposed to improve the convergence speed greatly. According to the individual evolutionary process, a self-learning mechanism is introduced to adapt the mutation constant and crossover probability constant. As a result, the robustness of the proposed algorithm is improved. To demonstrate the effectiveness of the proposed algorithm, three classical test cases are conducted and compared with four other intelligent optimization algorithms. The experiment results show that the proposed FSADE is an very effective algorithm for solving the power economic dispatch.