This paper investigates a novel recurrent neural network (NN)-based vector control approach for single-phase grid-connected converters (GCCs) with L (inductor), LC (inductor-capacitor) and LCL (inductor-capacitor-inductor) filters and provides their comparison study with the conventional standard vector control method. A single neural network controller replaces two current-loop PI controllers, and the NN training approximates the optimal control for the single-phase GCC system. The Levenberg⁻Marquardt (LM) algorithm was used to train the NN controller based on the complete system equations without any decoupling policies. The proposed NN approach can solve the decoupling problem associated with the conventional vector control methods for L, LC and LCL-filter-based single-phase GCCs. Both simulation study and hardware experiments demonstrate that the neural network vector controller shows much more improved performance than that of conventional vector controllers, including faster response speed and lower overshoot. Especially, NN vector control could achieve very good performance using low switch frequency. More importantly, the neural network vector controller is a damping free controller, which is generally required by a conventional vector controller for an LCL-filter-based single-phase grid-connected converter and, therefore, can overcome the inefficiency problem caused by damping policies.