In task decomposition and coordination for multi-robot, the problem of workload imbalance in task with partial order constraint still exists. To overcome this problem, a task coordination and workload balance method for multi-robot based on trading-tree was proposed. Firstly, the task decomposition problem satisfying partial order constraint was described as a constraint graph. Secondly, an initial task assignment strategy was proposed according to the directed weighted graph, and the problem of task coordination among multiple robots was solved by using the improved Dijkstra algorithm. At last, the strategy of workload balance was proposed to balance each robot's workload without violating any constraints via a protocol based on trading-tree. The experimental results show that, compared with Dijkstra algorithm, after finishing the strategy of workload balance, the efficiency signifiantly increases by 12% and the difference of workload reduces by 30%.