Millimeter-wave vehicle-to-vehicle communication systems with multiple-input multiple-output antenna array have drawn significant attention because it is expected to satisfy the growing bandwidth requirements for the cooperative intelligent transportation systems. However, maintaining high-quality communication links between communicating vehicles without high overhead is a challenging problem due to the high mobility of vehicles. In this paper, we propose a beam management algorithm with spatially distributed antenna subarrays instead of a single co-located antenna array. Unlike existing methods, we use distributed antenna subarrays to exploit the geometric relationship of the beam directions and the relative distance between communicating vehicles. We reduce the beam alignment errors by minimizing the sum of squared errors between the estimated beam direction after the beam training process and the refined beam direction derived from the measured position and velocity data. Additionally, a position data request protocol is devised to reduce the beam refining errors. Numerical results demonstrate that the proposed beam management algorithm successfully reduces the beam alignment errors and it is robust to position and velocity measurement errors.