In this paper, we investigate the effect of dissipation on the entanglement dynamics of a three-level atom in V-configuration with a two-mode quantized field in a cavity optomechanics system. To achieve the purpose, we first deduce the effective Hamiltonian and by the dissipation terms, we evaluate the explicit time-dependent form of the state vector of the whole system by choosing special initial conditions for atom, field and the oscillatory mirror. Then, we obtain the time evolution of atomic linear entropy as a measure of entanglement. The results show that the dissipation reduces the entanglement between the atom and the subsystem of field and mirror.