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With the development of intelligent traffic system, it is critical to use C-V2X to improve the safety of vehicles at intersections. In this paper, a C-V2X based cooperative intersection collision avoidance system is constructed and the safety performance of the system is analytically characterized. Specifically, the Poisson line process (PLP) model is used to describe the node location distribution. The communication outage probability and the intersection collision avoidance probability between two vehicles are derived. Then the probability of intersection collision warning that provides early warning service for the vehicles on the road is presented. Simulation results verify our analysis and reveal the impact of the system parameters on the network performance. This work provides theoretical support for the design and optimization of intelligent transportation based on C-V2X.