Sound speed profile (SSP) significantly affects acoustic propagation in the ocean. In this work, the SSP is inverted using compressive sensing (CS) combined with beamforming to indicate the direction of arrivals (DOAs). The travel times and the positions of the arrivals can be approximately linearized using their Taylor expansion with the shape function coefficients that parameterize the SSP. The linear relation between the travel times/positions and the shape function coefficients enables CS to reconstruct the SSP. The conventional objective function in CS is modified to simultaneously exploit the information from the travel times and positions. The SSP is estimated using CS with beamforming of ray arrivals in the SWellEx-96 experimental environment, and the performance is evaluated using the correlation coefficient and mean squared error (MSE) between the true and recovered SSPs, respectively. Five hundred synthetic SSPs were generated by randomly choosing the SSP dictionary components, and more than 80 percent of all the cases have correlation coefficients over 0.7 and MSE along depth is insignificant except near the sea surface, which shows the validity of the proposed method.