Low latency and energy efficiency are two important performance requirements in various fifth-generation (5G) wireless networks. In order to jointly design the two performance requirements, in this paper a new performance metric called effective energy efficiency (EEE) is defined as the ratio of the effective capacity (EC) to the total power consumption in a cellular network with underlaid device to device (D2D) communications. We aim to maximize the EEE of the D2D network subject to the D2D device power constraints and the minimum rate constraint of the cellular network. Due to the non-convexity of the problem, we propose a two-stage difference-of-two-concave (DC) function approach to solve this problem. Towards that end, we first introduce an auxiliary variable to transfer the fractional objective function into a subtractive form. We then propose a successive convex approximation (SCA) algorithm to iteratively solve the resulting non-convex problem. The convergence and the global optimality of the proposed SCA algorithm are both analyzed. The numerical results are presented to demonstrate the effectiveness of the proposed algorithm.