This article presents an algorithm termed as multiobjective dynamic rapidly exploring random (MOD-RRT*), which is suitable for robot navigation in unknown dynamic environment. The algorithm is composed of a path generation procedure and a path replanning one. First, a modified RRT* is utilized to obtain an initial path, as well as generate a state tree structure as prior knowledge. Then, a shortcuting method is given to optimize the initial path. On this basis, another method is designed to replan the path if the current path is infeasible. The suggested approach can choose the best node among several candidates within a short time, where both path length and path smoothness are considered. Comparing with other static planning algorithms, the MOD-RRT* can generate a higher quality initial path. Simulations on the dynamic environment are conducted to clarify the efficient performance of our algorithm in avoiding unknown obstacles. Furthermore, real applicative experiment further proves the effectiveness of our approach in practical applications.