We study the problem of hyperparameter tuning in sparse matrix factorization under a Bayesian framework. In prior work, an analytical solution of sparse matrix factorization with Laplace prior was obtained by a variational Bayes method under several approximations. Based on this solution, we propose a novel numerical method of hyperparameter tuning by evaluating the zero point of the normalization factor in a sparse matrix prior. We also verify that our method shows excellent performance for ground-truth sparse matrix reconstruction by comparing it with the widely used algorithm of sparse principal component analysis.