In this paper, we propose a QAPM(Quadrature Amplitude Position Modulation) modulation using compressive sensing for the purpose of power efficiency improvement. QAPM modulation is a combination technique of QAM (quadrature amplitude modulation) and PPM(Pulse Position Modulation). Therefore it can decrease the transmission power and improve BER performance. Moreover, even if the band width is widened when the number of positions is increased, high sparsity characteristic caused by position number can be applied to compressive sensing technique. Compressive sensing has recently studied as a method that can be successfully reconstructed from the small number of measurements for sparse signal. Therefore, the proposed system can lower price of receiver by reducing sampling rate and has performance improved by using QAPM modulation. And the results are confirmed through simulations.