In this paper, a new cuckoo search algorithm with gravitational acceleration search mechanism is presented to address low convergence rate and deteriorated search precision. The algorithm is fundamentally inspired by the fact that gravitational search can also get the global optimal without perceiving the change on the driving effect of external environment. Each of the cuckoo nests exerted on different quality not only follows the Levy flight law but also abides the law of universal gravitation during the process of optimization, which accelerates the convergence significantly due to the intrinsic gravitational attraction between individuals within the cuckoo nests. Furthermore, a new probability mutation approach is formally given to achieve a balance between the global and local search for the proposed algorithm. Consequently, the global convergence efficiency and search precision of the algorithm are significantly enhanced. Via mathematical analysis and 26 benchmark test functions, the proposed agorithm is competitive for the convergence rate and search precision in a comparison with other variants of intelligent optimization algorithm.