Connected vehicles have received much attention in recent years due to their significant societal benefit and commercial value. However, a suitable channel model for vehicle-to-vehicle (V2V) communications is difficult to build due to the dynamic communication environment. In this paper, a three-dimensional (3D) geometrical propagation model that includes line-of-sight (LoS), single bounced (SB), and multiple bounced (MB) rays is proposed. Each of multiple scatterers in the model is moving with a random velocity in a random direction. Based on the geometrical propagation model, a generalized 3D reference model for narrowband multiple-input-multiple-output (MIMO) V2V multipath fading channels is developed. The corresponding space-time correlation functions (ST-CFs), time correlation functions (T-CFs), and space correlation functions (S-CFs) are analytically investigated and numerically simulated in terms of various factors. Several notable ST-CFs for V2V and fixed-to-mobile (F2M) communications become the special cases of ST-CFs of the proposed model by adjusting the corresponding channel parameters. Finally, the theoretical results of the space-Doppler power spectral density (SD-PSD) are compared with the available measured data. The close agreements between the theoretical and measured SD-PSD curves confirm the utility and generality of the proposed model.