The realization of photon-photon quantum teleportation based on cavity optomechanical system has made important progress. Nevertheless, transmitting the photon's quantum state that are convenient for transmission to phonon with long lifetime via quantum teleportation is still an challenging issue that awaits resolution. Based on the hybrid cavity optomechanical system, a physical implementation scheme for the nonlocal transmission of unknown quantum states solid-state qubits and flying qubits through nonlinear interaction is proposed. In order to explore the feasibility of the scheme, the influence of temperature and cavity dissipation on the fidelity of hybrid quantum teleportation between phonon and photon is considered. The results show that high-fidelity hybrid quantum teleportation between phonon and photon can be realized by adjusting appropriate parameters under certain temperature and dissipation conditions, which has high theoretical significance in non-local hybrid quantum information processing.