Automatic modulation classification (AMC) is one of the most essential algorithms to identify the modulation types for the non-cooperative communication systems. Recently, it has been demonstrated that deep learning (DL)-based AMC method effectively works in the single-input single-output (SISO) systems, but DL-based AMC method is scarcely explored in the multiple-input multiple-output (MIMO) systems. In this correspondence, we propose a convolutional neural network (CNN)-based cooperative AMC (Co-AMC) method for the MIMO systems, where the receiver equipped with multiple antennas cooperatively recognizes the modulation types. Specifically, each received antenna gives their recognition sub-results via the CNN, respectively. Then, the decision maker identifies the modulation types with the recognition sub-results and cooperative decision rules, such as direct voting (DV), weighty voting (WV), direct averaging (DA) and weighty averaging (WA). The simulation results demonstrate that the Co-AMC method, based on the CNN and WA, has the highest correct classification probability in the four cooperative decision rules. In addition, the CNN-based Co-AMC method also performs better than the high order cumulants (HOC)-based traditional AMC methods, which shows the effective feature extraction and powerful classification capabilities of the CNN.