A Cooperative Adaptive Cruise Control (CACC) algorithm based on Model Predictive Control (MPC) and an improved spacing policy is proposed in this study to address the current issues of low road utilization and inadequate dynamic regulation during platoon driving. First and foremost, the state of the leader vehicle and the minimum safe following distance are incorporated into the spacing policy to create an enhanced constant time headway (CTH) spacing policy. Secondly, following the MPC principle, the optimization problem of vehicle platoon is converted into a constrained quadratic programming problem that fulfills the requirements of driving safety, following distance, and ride comfort in a platoon. Finally, six-homogeneous-vehicle platoon is constructed for simulation verification, and the results show that the designed algorithm can not only ensure the string stability of platoon, but also effectively improve the road utilization rate. And in the vehicle of platoon cut-in/cut-out conditions, CACC is proven to have good ability of dynamically adjusting and restoring platoon stability.