Device-to-device (D2D) communication enables two local users to communicate with each other directly instead of relaying through a third party, e.g., base station. In this paper, we study a subchannel sharing strategy underlaying multichannel cellular network for D2D pairs and existing cellular users (CUs). In the investigated scenario, we try to improve the spectrum efficiency of D2D pairs, but inevitably brings cross interference between two user groups. To combat interference, we attempt to assign each D2D pair with appropriate subchannels, which may belong to different CUs, and manipulate transmission power of all users so as to maximize the sum rate of all D2D pairs, while assuring each CU with a minimum data rate on its subchannel set. The formulated problem is a nonconvex problem and thus, obtaining its optimal solution is a tough task. However, we can find optimal power and subchannel assignment for a special case by setting an independent data rate constraint on each subchannel. Then we find an efficient method to calculate a gradient for our original problem. Finally, we propose a gradient-based search method to address the problem with coupled minimum data rate constraint. The performance of our proposed subchannel sharing strategy is illustrated via extensive simulation results.