The rapid development and integration of automotive manufacturing, sensor, and communication technologies have facilitated the emergence of the Internet of Vehicles (IoV). However, the explosive growing demand for parking spots has become a challenging issue to be addressed in IoV. In this paper, we propose a novel Smart Parking System (SPS) for IoV by applying the matching game approach. Specifically, the proposed SPS consists of three types of entities: drivers, parking spot owners (PSOs), and a certificate authority (CA). Drivers and PSOs send parking requests and parking spot information to the CA, respectively. The CA is responsible for identifying legitimate system users, matching drivers with PSOs, and recording their transaction information. We first design rational utility functions for drivers and PSOs, and then establish preference lists for them based on real-time conditions. With these information, we further develop an improved marriage matching (MM) algorithm to achieve stable matching results for drivers' requests and parking spot allocation. Simulation results demonstrate that the proposed MM-based SPS not only ensures stable matching results with the objective of distance minimization but also achieves an overall utility close to that of the optimal algorithm.