Agent-based moving source-seeking problem with strategic control considering obstacle avoidance is addressed in this paper. The agents communicate with one another using a communication topology to coordinate finding the object. The source or seeking target is represented by a scalar field, whereas the presence of the obstacle is represented by an artificial potential field. A moving source that moves linearly from the initial point to the end point is considered. Several obstacles, which needs to be avoided by agents, that may be stationary or moving are considered. Double integrator agents are considered, which contains richer dynamics compared to the single integrator agents. The strategic control law which is a combination of gradient consensus and distributed velocity control affected by artificial potential field are used to determine the velocity of each agent to track the moving source while avoiding the obstacles. Formation control is used to make sure that the agents stay under the desired formation for most of the time. The computer simulation is used to examine how different agents would search for a moving source under stationary and moving obstacles. In both cases, the agents can find the source with a different seeking time: 62.8s for stationary and 90s for moving obstacles. Comparing with virtual artificial potential field method, our proposed method manages to perform better in the case of shrinking agents for stationary obstacles.