Enhancing the fidelity of quantum state transmission in noisy environments is a significant subject in the field of quantum communication. In this paper, improving the fidelity of a deterministic remote state preparation (RSP) protocol under decoherence is investigated with the technique of weak measurement (WM) and weak measurement reversal (WMR). We first construct the quantum circuit of the deterministic remote preparation of a single-qubit state through an EPR state with the assistance of an auxiliary qubit. Then, we analytically derive the average fidelity of the deterministic RSP protocol under the influence of generalized amplitude damping noises acting on the EPR state. Our results show that when only qubit 2 undergoes the decoherence channel, the average fidelity of the RSP protocol subject to generalized amplitude damping noise is the same as that subject to amplitude damping noise. Moreover, we analyze the optimal average fidelity of the above RSP process by introducing WM and WMR. It is found that the application ofWMand a subsequent reversal operation could lead to the remarkable improvement of the average fidelity for most values of the decoherence parameters.