This paper proposed a Triangular Inequality based rewiring method for the RRT(Rapidly exploring Random Tree)-Connect robot path planning algorithm that guarantees the convergence time than the RRT algorithm, to enhance the optimality. To check the performance of the proposed algorithm, this paper compared with the RRT and RRT-Connect algorithms in various environments through simulation. From these experimental results, the proposed algorithm shows both quick convergence time and better optimality than the RRT algorithm, and more optimal than RRT-Connect algorithm with the similar number of sampling and convergence time.