For diverse three-node vertical-cavity surface-emitting laser (VCSEL) networks, a new criterion of the globally complete chaos synchronization (GCCS) among all node lasers is proposed by using the master-stability function (MSF). It is found that GCCS can be achieved for an arbitrarily given three-node VCSEL networks when two points determined by constant row sum and two transversal eigenvalues fall into the region of stability where maximum Lyapunov exponent (MLE) is negative and the MLE as a function of constant row sum and the eigenvalue associated to perturbations within the synchronization manifold is positive. The criterion can be generalized to multiple (more than four) nodes VCSEL networks. Based on the theoretical criterion and synchronization error theory, the synchronization properties in three-node VCSEL network with the ring topology are further explored. As a result, the theoretical criterion is in excellent agreement with the numerical results, which indicate that the theoretical criterion is valid and feasible.