This paper addresses the formation control problem of multi-agent systems whose dynamics are all positive. Recently, as a byproduct of the analysis of interconnected positive systems, we have shown an effective way for designing a communication scheme (i.e., an interconnection matrix) over the positive agents so that a prescribed formation can be achieved. For the convergence rate analysis of such multi-agent positive systems under formation control, we propose an efficient algorithm to compute the dominant pole of interconnected positive systems by actively using the positive property of each agent. We illustrate by numerical examples that the proposed algorithm is definitely efficient particularly when the number of agents gets larger.