In this paper, we propose a novel adaptive beamforming algorithm for coprime array by compressive sensing the virtual uniform linear array signal. Based on the idea of coprime sampling, a much longer virtual uniform linear array can be generated from a coprime array. With a compressive sensing matrix, a connection can be built between the coprime array with fewer physical sensors and the virtual uniform linear array with much more virtual sensors. Hence, the proposed adaptive beamforming algorithm takes full advantage of the longer virtual array. The performance increment provided by the virtual array is much larger than the performance loss due to the introduced compressive sensing. Hence, the beam-former using the virtual array is expected to obtain much better performance than those using the coprime array directly. Simulation results demonstrate the effectiveness of the proposed adaptive beamforming algorithm.