Next-generation (5G) cellular networks must deal with massive Machine-Type Communications (MTC) for Internet of Things applications. Because of the potentially large number of coexisting MTC devices, achieving efficient device management and signaling is an essential issue. Moreover, many MTC devices are battery-operated and require a long battery life. It is difficult to achieve low power consumption using MTC devices with limited control signaling overhead. To accomplish this, this study proposes a group-based power-control scheme. To reduce signaling overhead, the proposed scheme assigns one ID and one power-control parameter to a group of MTC links that are allocated on the same resource block. To maintain low power consumption, we formulate a resource allocation problem that aims to minimize the power consumed by MTC links. We propose a greedy algorithm to solve this problem. Numerical results show that the proposed scheme can achieve low power consumption and low signaling overhead.