Full-scanned photoacoustic data of the sample are needed to achieve better quality of the reconstructed photoacoustic image with filtered back projection algorithm. However, such a requirement is usually difficult to be satisfied due to the restrictions of the hardware conditions and spatial size. To tackle such a problem, a compressed sensing based method was proposed to recover the full-scanned photoacoustic data from the incomplete measurements. The results from the numerical simulation demonstrates that both the mean squared error and the peak signal-to-noise ratio(PSNR) of the image can significantly improved with our proposed method.