This study aims to analyze the impact of connected and autonomous vehicles (CAVs) on traffic safety under various penetration rates. Based on a recently proposed heterogeneous flow model, the mixed traffic flow with both conventional vehicles and CAVs was simulated and studied. The frequency of dangerous situations and value of time-to-collision in the mixed traffic flow under different CAV penetration rates was calculated and used as indicators of CAV's impact on traffic safety. Acceleration rate and velocity difference distribution of the mixed traffic flow was presented to show the evolution of mixed traffic flow dynamics with the increase in CAV penetration rates within the mixed flow. Results show that the condition of traffic safety is greatly improved with the increase in the CAV penetration rate. More cautious car-following strategy of the CAV would contribute to a greater benefit on traffic safety, though less gain in capacity. With the increase in CAV penetration rate, the portion of smooth driving is increased. Velocity difference between vehicles is decreased and traffic flow is greatly smoothed. Stop-and-go traffic will be greatly eased. (C) 2019 Elsevier B.V. All rights reserved.