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This paper investigates power allocation for D2D communications in a Heterogeneous Network (HetNet)which includes a macro cell and pico cells, whereas femto cells are distributed inside. The objective is tominimize the total power consumption of D2D transmitter while satisfying a set of Quality of Service inD2D receivers and cellular users communication interference. To this end, we first obtain expression for theformula of signal to interference plus noise ratio (SINR) and spectral efficiency of each D2D receiver. Then,an optimization problem is formulated to minimize the total transmit power of D2D transmitters subject toQoS constraints. It is shown that this optimization problem is linear programming and it can be solved inpolynomial time with standard tools. In addition, the maximization value of D2D pair transmission rates aredetermined with fixed cellular users parameters.