In this paper, we present the computation-efficient resource allocation (RA) schemes for millimeter-wave mobile edge computing (mmWave-MEC) system with the aid of reconfigurable intelligent surface (RIS), which is used to assist the uplink communication from the users to the base station (BS). By means of the theoretical analysis, the achievable rate and computation efficiency (CE) are derived. Then, the optimization problem for the CE maximization under the constraints of the minimum rate, maximum power consumption and local CPU frequency is formulated, where the joint design of the hybrid beamforming at the BS and the passive beamforming at the RIS as well as the local resource allocation of each user is carried out. An effective iterative algorithm based on the penalized inexact block coordinate descent (BCD) method is proposed to obtain the computation-efficient RA scheme. Next, a low-complexity suboptimal RA scheme based on the BCD method is proposed, and corresponding algorithm is presented. Simulation results show that the proposed schemes are effective, and high CE can be attained. Moreover, the second scheme can achieve the CE performance close to the first scheme but with lower complexity. Besides, it is effective to deploy the RIS scheme in mmWave-MEC system, which can strike a balance between the CE and energy consumption when compared to the conventional relay schemes.