Device-to-device (D2D) communication has been considered as a promising technique to meet the challenging requirements in the fifth generation (5G) cellular networks. Traditional power control schemes mainly focused on delay-unaware metrics, such as throughput and power consumption, thus being only efficient for delay-insensitive applications. To overcome this problem, we in this paper propose an effective power control scheme for D2D communications underlaying cellular networks while satisfying heterogeneous statistical quality-of-service (QoS) requirements. Specifically, we formulate a constraint optimization problem which aims at maximizing the cellular user's effective capacity while meeting the D2D pair's effective capacity constraint. By using convex approximation, we convert the original non-convex optimization problem into a strictly convex one and derive the optimal solution via the Lagrangian approach. We conduct intensive simulations and analyze the impacts of different factors, such as the stringency of QoS requirements and the interference levels, on the system performance.