Recently, device-to-device (D2D) communication in cellular networks has gained much attention for enabling a base station (BS) to offload traffic to direct D2D links and for facilitating new network services. In this paper, we propose a semi-distributed resource allocation scheme for the D2D communication where the BS allocates radio resources for cellular user links and D2D links in a centralized manner while the modulation and coding scheme (MCS) level and the transmission power of D2D links are distributively decided by the device of each D2D link. We first formulate a resource allocation problem of which the objective is to maximize the spatial reuse of radio resources by allowing the simultaneous transmission of D2D links on the same resources. To solve the problem, we present a suboptimal greedy algorithm. By simulation, we show that the cellular networks with the proposed scheme achieve a higher network throughput by maximizing the spatial reuse of radio resources.