We investigate the influence of decoherence of entanglement on the deterministic remote state preparation. Firstly, the determinability and the depletion of entanglement bits and classical bits are obtained. Then two kinds of decoherent channels (depolarizing and dephasing) are analyzed. For the depolarizing channel, the fidelity is related only to the depolarization and the latitude of target quantum bits on the Bloch sphere, but is independent of longitude. For the dephasing channel, the fidelity is not affected by the quantum channel and only related to the latitude of target quantum bits.