Based on the 2x2 (electric field) cross-spectral density matrix, a model for an electromagnetic J0-correlated Schell-model beam is given that is a generalization of the scalar J0-correlated Schell-model beam. The conditions that the matrix for the source to generate an electromagnetic J0-correlated Schell-model beam are obtained. The condition for the source to generate a scalar J0-correlated Schell-model beam can be considered as a special case.