In this paper, we firstly propose a joint subcarrier and power allocation approach for multi-user integrated visible light communication and positioning (VLCP) systems in the presence of practical unique optical constraints. The purpose of the proposed resource allocation approach is to maximize the sum rate of users and meanwhile guarantee the different minimum data rates and positioning accuracy requirements of users. Then, we solve the optimization problem by decomposing it into two subproblems, where a low-complexity suboptimal subcarrier allocation approach is proposed and the sequential quadratic programming (SQP) method is adopted to solve the non-linearly constrained power allocation optimization problem. Numerical results show that the proposed resource allocation approach can effectively improve the sum rate and the positioning accuracy of users compared with other resource allocation approaches.