We consider the problem of coordinating a set of automated vehicles at an intersection with no traffic light. The priority-based coordination framework is adopted to separate the problem into a priority assignment problem and a vehicle control problem under fixed priorities. This framework ensures good properties like safety (collision-free trajectories, brake-safe control) and liveness (no gridlock). We propose a decentralized Model Predictive Control (MPC) approach where vehicles solve local optimization problems in parallel, ensuring them to cross the intersection smoothly. The proposed decentralized MPC scheme considers the requirements of efficiency, comfort and fuel economy and ensures the smooth behaviors of vehicles. Moreover, it maintains the system-wide safety property of the priority-based framework. Simulations are performed to illustrate the benefits of our approach.