Connected and autonomous vehicles (CAVs) can realize many revolutionary applications, but it is expected to have mixed-traffic including CAVs and human-driving vehicles (HVs) together for decades. In this paper, we target the problem of mixed-traffic intersection management and schedule CAVs to control the subsequent HVs. We develop a dynamic programming approach and a mixed integer linear programming (MILP) formulation to optimally solve the problems with the corresponding intersection models. We then propose an MILP-based approach which is more efficient and real-time-applicable than solving the optimal MILP formulation, while keeping good solution quality as well as outperforming the first-come-first-served (FCFS) approach. Experimental results and SUMO simulation indicate that controlling CAVs by our approaches is effective to regulate mixed-traffic even if the CAV penetration rate is low, which brings incentive to early adoption of CAVs.