Abstract: In recent years, a family of methods based on integral correction have been developed to address the increasing requirements of accuracy and efficiency of orbit computation in aerospace engineering. These methods are fast and accurate via integral correction in a large domain, but limited by scarceness of computing resources in serial computing environment. The serial computing is essentially a waste of the advantage of the integral correction type methods which can support parallel computing. In addition, the appropriate calculation parameters of these methods are usually difficult to determine. That makes it difficult to to choose a proper large step size to ensure both accuracy and efficiency. For the above issues, a parallel accelerated local variation iteration method (PA-LVIM) is presented in this paper based on the local variation iteration method (LVIM) which is a classical method based on integral correction. By exploiting parallel computing, the amount of computational burden in the LVIM is distributed to multiple computing nodes so as to accelerate the computing speed. In addition, the calculation parameters of the PA-LVIM are optimized by a novel polishing mesh refinement method, which divides the integration stepsize according to the second derivatives of the dynamic system states. Three classical orbit propagation problems are solved to verify the validity of the proposed PA-LVIM. Simulation results show that the PA-LVIM is dramatically accelerated, and its computational efficiency is further improved in combination with the polishing mesh refinement method, which increases the efficiency of current methods by more than 5 times.