Millimeter wave (mmWave) communication is a promising technology to alleviate the shortage of spectrum resources in vehicular networks. To use mmWave spectrum resources more efficiently, in this paper we propose a novel beam alignment-based vehicular mmWave spectrum sensing model and algorithm. We first establish the spectrum sensing model on the basis of characteristics of mmWave signals and then derive the test statistics. Based on the sensing model, the beam alignment-based vehicular mmWave spectrum sensing (BA-VMSS) algorithm is proposed by utilizing the temporal correlation of the sensing data caused by vehicular movement. As a result, the probability of detection is derived. Simulation results validate the efficiency of the proposed algorithm.