Due to the requirements for mobile robots to search or rescue in unknown environments, reactive navigation which plays an essential role in these applications has attracted increasing interest. However, most existing reactive methods are vulnerable to local minima in the absence of prior knowledge about the environment. This paper aims to address the local minimum problem by employing the proposed boundary gap (BG) based reactive navigation method. Specifically, the narrowest gap extraction algorithm (NGEA) is proposed to eliminate the improper gaps. Meanwhile, we present a new concept called boundary gap which enables the robot to follow the obstacle boundary and then get rid of local minima. Moreover, in order to enhance the smoothness of generated trajectories, we take the robot dynamics into consideration by using the modified dynamic window approach (DWA). Simulation and experimental results show the superiority of our method in avoiding local minima and improving the smoothness.