The millimeter wave (mmWave) communication has drawn intensive attention with abundant band resources. In this paper, we consider the popular content distribution (PCD) problem in the mmWave vehicular network. In order to offload the communication burden of base stations (BSs), vehicle-to-vehicle (V2V) communication is introduced into the PCD problem to transmit contents between on-board units (OBUs) and improve the transmission efficiency. We propose a full-duplex (FD) cooperative scheme based on coalition formation game, and the utility function is provided based on the maximization of the number of received contents. The contribution of each member in the coalition can be transferable to its individual profit. While maximizing the number of received contents in the fixed time, the cooperative scheme also ensures the individual profit of each OBU in the coalition. We evaluate the proposed scheme by extensive simulations in mmWave vehicular networks. Compared with other existing schemes, the proposed scheme has superior performances on the number of possessed contents and system fairness. Besides, the low complexity of the proposed algorithm is demonstrated by the switch operation number and CPU time.