This paper proposes a new approach for nonrigid structure from motion with occlusion, based on sparse representation. We address the occlusion problem based on the latest developments on sparse representation: matrix completion, which can recover the observation matrix that has high percentages of missing data and can also reduce the noises and outliers in the known elements. We introduce sparse transform to the joint estimation of 3-D shapes and motions. 3-D shape trajectory space is fit by wavelet basis to achieve better modeling of complex motion. Experimental results on datasets without and with occlusion show that our method can better estimate the 3-D shapes and motions, compared with state-of-the-art algorithms.