The Preisach hysteresis model has been adopted extensively in magnetic and smart material-based systems. Fidelity of the model hinges on accurate identification of the Preisach density function. Existing work on the identification of the density function usually involves applying an input that provides sufficient excitation and measuring a large set of output data. In this paper, we propose a novel compressive sensing-based approach for Preisach model identification that requires fewer measurements. The proposed approach adopts the discrete cosine transform of the output data to obtain a sparse vector, where the order of all the output data is assumed to be known. The model parameters can be efficiently reconstructed using the proposed scheme. For comparison purposes, a constrained least-squares scheme using the same number of measurements is also considered. The root-mean-square error is adopted to examine the model identification performance. The proposed identification approach is shown to have better performance than the least-squares scheme through both simulation and experiments involving a vanadium dioxide (VO2)-integrated microactuator.