This paper presents a new approach to solve the pursuit problem based on a univector field method. In our proposed method, a set of eight agents works together instantaneously to find suitable moving directions and follow the univector field to pursue and capture a prey agent by surrounding it from eight directions in an infinite grid-world. In addition, a set of strategies is proposed to make the pursuit problem more realistic in the real world environment. This is a general approach, and it can be extended for an environment that contains static or moving obstacles. Experimental results show that our proposed algorithm is effective for the pursuit problem.