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This paper provides an alternating optimization algorithm for large-scale matrix rank minimization problems and its parallel implementation on GPU. The matrix rank minimization problem has a lot of important applications in signal processing, and several useful algorithms have been proposed. However most algorithms cannot be applied to a large-scale problem because of high computational cost. This paper proposes a null space based algorithm, which provides a low-rank solution without computing inverse matrix nor singular value decomposition. The algorithm can be parallelized easily without any approximation and can be applied to a large-scale problem. Numerical examples show that the algorithm provides a low-rank solution efficiently and can be speed up by parallel GPU computing.