As a promising wireless communication technique, Device-to-Device (D2D) can improve the utilization of spectrum resources, overall system throughput and reduce end-to-end delay, energy consumption by exploiting the direct radio link between local devices. Meanwhile, introducing D2D in cellular networks is very challenging due to the complex interference problem. To deal with the complex interference of D2D Underlying Cellular Networks, Interference alignment (IA) as an efficient interference management technique is extensively studied for D2D communications underlaying the cellular networks. However, most of the previous researches on IA only consider the equal power allocation for users, which leads to suboptimal overall system throughput. In order to further improve the system performance, in this paper, we propose a joint power allocation based on stackelberg game and interference alignment algorithm (STPA-IA) to eliminate the complex interference in D2D communications underlaying cellular networks. In this joint approach, the base station (BS) is modeled as the leader while the D2D pairs are followers. The performance of network system and that of D2D users are regarded as the revenues of leader and followers in stackelberg game. The strategy of the leader (BS) is to get the maximum benefits by reducing the interference, while the followers tend to (D2D pairs) maximize their own utility according to leader's strategy. The non-cooperative game is proved to get the nash equilibrium by the above strategies. Moreover, the close-form expression of the allocated power by maximum the unity function of leader and followers is derived. Extensive simulation results demonstrate that the proposed algorithm outperforms previous works in terms of sum-rate with lower time complexity.