In this paper, we consider the three-dimensional (3D) differential microwave imaging for brain stroke monitoring. Assuming that stroke causes small changes in the electromagnetic parameters of the head, we apply the Distorted Born approximation to linearize the scattering equation. To exploit the sparse nature of the problem, we develop an imaging algorithm based on the compressive sensing. The algorithm was able to locate the stroke and accurately estimate its shape even with limited prior knowledge such as average head permittivity. In addition, we have compared the obtained results with those computed using the truncated singular value decomposition (TSVD).