In this paper, local learning is proposed to improve the speed and the accuracy of convergence performance of regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA), a typical multi-objective optimization algorithm via estimation of distribution. RM-MEDA employs a model-based method to generate new solutions, however, this method is easy to generate poor solutions when the population has no obvious regularity. To overcome this drawback, our proposed method add a new solution generation strategy, local learning, to the original RM-MEDA. Local learning produces solutions by sampling some solutions from the neighborhood of elitist solutions in the parent population. As it is easy to search some promising solutions in the neighborhood of an elitist solution, local learning can get some useful solutions which help the population attain a fast and accurate convergence. The experimental results on a set of test instances with variable linkages show that the implement of local learning can accelerate convergence speed and add a more accurate convergence to the Pareto optimal.