Abstract: For the reconstruction problem of inhomogeneous scatterers, a Bayesian compressive sensing microwave imaging method based on Born approximation is proposed. In the framework of first-order Born approximation, a sparse sensing model is established based on the electric field integral equation and the mesh discretization in the imaging region. Then a Bayesian probability density function based on Gaussian Prior is constructed, and the objective function is optimized by using the relevant vector machine method. Finally, the microwave imaging of the target is realized. By studying the microwave imaging of multi-pixel single target, non-uniform single target and non-uniform multi-target and by considering the noise impact in the numerical example, the result is obtained and shows that the reconstruction result of Bayesian compressive sensing method based on Gaussian Prior is better than that of conjugate gradient iterative algorithm and orthogonal matching pursuit compressive sensing reconstruction algorithm, thus it verifies the effectiveness and robustness of the proposed method.