This chapter discusses research issues related to agent-based Grid computing. Grid computing now becomes an innovative computing paradigm and helps build non-traditional computing infrastructures and applications. Multiple-agent systems and algorithms, on the other hand, mainly focus on solving corporative problems among multiple participants, mainly from theoretical aspects. It is thus a natural choice to combine these two key technologies together and benefit both research communities. This chapter first reviews background for multi-agent system, agent-based computing, and Grid computing. Research challenges and issues are characterized and identified together with possible solutions. After the investigation of current research efforts of agent-based Grid computing, future research trends are presented and studied.