This paper proposes a bidirectional platoon control law using a coupled distance error based on the backstepping-like feedback linearization control method for an interconnected mobile agent system with a string structure. Unlike the previous results where the single agent was controlled using the only own information without other agents, the proposed control law cannot show the only distance error convergence of each agent, but also the string stability of the whole system. Also, the control performances are improved by the proposed control law in spite of low performance of bidirectional control strategy in the previous results. The proposed bidirectional platoon control algorithm is based on the backstepping-like feedback linearization control method. The position errors between each agent and the preceding and the behind agents are coupled by weighted summation. By the proposed control law, the distance error of each agent can converge to zero while the string stability is guaranteed when the coupled errors can converge to zero. To this end, the back-stepping control method is employed. The pseudo velocity input is determined considering the kinematic relationship between agents and the string stability. Then, the actual dynamic control input is determined to make the actual velocity converge to the pseudo velocity input. The stability analysis and the simulation results of the proposed method are included in order to demonstrate the practical application of the proposed algorithm.