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The cooperative control of marine vehicles finds wide applications in many marine missions and tasks. This paper investigates the receding horizon formation tracking control problem of a fleet of underactuated autonomous underwater vehicles (AUVs), in which the follower AUVs are required to track the leader with prescribed formation pattern, and the control inputs of the follower AUVs are subject to practical constraints. An auxiliary stabilizable control law is first designed, based on which a novel optimization problem is proposed and a new receding horizon control (RHC) algorithm is designed to generate control inputs. The theoretical feasibility conditions of the RHC-based tracking algorithm and the stability conditions of the closed-loop systems are provided. Simulation studies are conducted, and the simulation results verify the effectiveness of the proposed algorithm and theoretical results.