In this work, we address the problem of low-rank matrix recovery from its under-sampled projections. The recovery is formulated as a Schatten-p norm minimization problem. We proposed a novel algorithm to solve the Schatten-p norm minimization problem based on the FOCUSS (FOCally Under-determined System Solver) approach. We compared our proposed method with state-of-the-art solvers. Experimental evaluation was carried out on two problems - matrix completion and image inpainting. For matrix completion, our proposed method showed better recovery rate than other methods. In the image inpainting problem, our method yields 1.5 dB improvement over the nearest competing algorithm.