In this paper, we propose an alternating minimization algorithm with an automatic selection of the regularization parameter for image reconstruction of photon-counted images. By using the generalized cross-validation technique, the regularization parameter can be updated in the iterations of the alternating minimization algorithm. Experimental results show that our proposed algorithm outperforms the two existing methods, the maximum likelihood expectation maximization estimator with total variation regularization and the primal dual method, where the parameters must be set in advance.