Deadbeat control (DBC) is developed based on the system model, which is commonly used to achieve good control performance for a three-phase grid connected converter (GCC). Unbalanced grid voltage is a common phenomenon in power systems. In this study, an improved DBC based on current predictive correction (CPC_DBC) is used to control GCC under an unbalanced grid voltage. The main purposes of CPC_DBC are to reduce the adverse effects due to random sampling error to improve current control performance, and to enhance the interference rejection capability of the control system. Then, the characteristics of CPC_DBC and the conventional DBC (Con_DBC) are analyzed by transfer functions in the discrete time domain. Several common control objectives under an unbalanced grid voltage are used to demonstrate the superiority of CPC_DBC. Finally, the experimental results indicate that CPC_DBC can effectively reduce the adverse effects of random sampling error; the robustness of system due to the uncertain value of the filter inductance is improved as well.