In this paper, we review the research on acceleration convergence approaches of evolutionary computation (EC) and its concrete application in the academy and industry. Evolutionary computation uses iterative progress, which is often inspired by biological mechanisms of evolution, to solve the problems that are multi-modal, multi-objective, discontinuous, non-differential, noisy and not well-defined. In this survey, many acceleration approaches are summarized and clustered in recent two decades. Applications of the acceleration approaches are included. We propose three promising research directions and their concrete approaches. These include including search space landscape approximation, search space projection and search strategy study, and comprise the main further research directions to be implemented an efficient EC search. Finally, we discuss the future research on accelerating convergence approaches of EC, and motivate some new approaches.