Target search and trapping using self-organized swarm robots have received increasing attention in recent years but control design of these systems remains a challenge. In this paper, we propose a decentralized control algorithm of swarm robot for target search and trapping inspired by bacteria chemotaxis. First, a local coordinate system is established according to the initial positions of the robots in the target area. Then the target area is divided into Voronoi cells. After the initialization, swarm robots start performing target search and trapping missions driven by the proposed bacteria chemotaxis algorithm under the guidance of the gradient information defined by the target. Simulation results demonstrate the effectiveness of the algorithm and its robustness to unexpected robot failure. Compared with other commonly used methods for distributed control of swarm robots, our simulation results indicate that the bacteria chemotaxis algorithm exhibits less vulnerability to local optimum, and high computational efficiency.