Vehicle-to vehicle (V2V) is one of the most challenging scenarios in the fifth-generation (5G) millimeter-wave (mmW) mobile communication networks. Existing models cannot be utilized without development for compatibility with modern measurements, which have proved that the wide-sense stationary (WSS) modeling assumption is valid only for very short intervals. In this paper, a novel three-dimensional (3D) geometry-based stochastic model (GBSM) for non-stationary (non-WSS) narrowband V2V multi-input-multi-output (MIMO) channel with both 3D fixed and moving scatterers around the transmitter (Tx) and the receiver (Rx) is proposed. The azimuth angle of departure (AAoD), elevation angle of departure (EAoD), azimuth angle of arrival (AAoA) and elevation angle of arrival (EAoA) of the 3D moving scatterers have been considered as time varying angles, and this makes the model non-stationary. Based on the proposed model, the statistical properties, including space-time correlation function (STCF), space-Doppler power spectral density (SD-PSD), level crossing rate (LCR), and average fade duration (AFD) are derived and compared with those of measured data and state-of-the-art channel models. Finally, the close agreement between results reveal that the proposed 3D model with 3D moving scatterers reflects the real-world V2V channel characteristics, especially in 5G mmW networks.