Mobile edge computing (MEC) has been regarded as a promising technique to support latencysensitivity and computation-intensive serves. However, the low offloading rate caused by the random channel fading characteristic becomes a major bottleneck in restricting the performance of the MEC. Fortunately, reconfigurable intelligent surface (RIS) can alleviate this problem since it can boost both the spectrum- and energy- efficiency. Different from the existing works adopting either fully active or fully passive RIS, we propose a novel hybrid RIS in which reflecting units can flexibly switch between active and passive modes. To achieve a tradeoff between the latency and energy consumption, an optimization problem is formulated by minimizing the total cost. In light of the intractability of the problem, we develop an alternating optimization-based iterative algorithm by combining the successive convex approximation method, the variable substitution, and the singular value decomposition (SVD) to obtain sub-optimal solutions. Furthermore, in order to gain more insight into the problem, we consider two special cases involving a latency minimization problem and an energy consumption minimization problem, and respectively analyze the tradeoff between the number of active and passive units. Simulation results verify that the proposed algorithm can achieve flexible mode switching and significantly outperforms existing algorithms.