With the development of communication and computation technologies, mobile edge computing (MEC) has become an emerging technology being deployed in 5G/B5G mobile networks to improve the mobile user experience. In this paper, we study the asymptotic performance of parallel computing in MEC networks with massive multi-input and multi-output (MIMO) in the millimeter wave band. First, a massive MIMO enabled MEC network with a parallel-limited computing model is constructed, and the task completed probability is defined as a new network performance metric. In the proposed model, we derive the task offloading and computing probabilities via the probability generation functional of the Poisson point process, from which, the task completed probability is obtained. Then we propose a computing resource allocation optimization algorithm to maximize the task completed probability within a given delay constraint. The numerical simulation results prove the accuracy of the obtained theoretical results and verify the performance of the proposed algorithm.