A scheme of strong coupling between the double electron spins and the quantized nano-mechanical harmonic oscillator is proposed based on the diamond nitrogen vacancy (NV) color center. A two-dimensional entangled state of two qubits is prepared by using the dissipative process of the nano-mechanical harmonic oscillator. The numerical simulation results show that, all the systems with different initial states can evolve to the target states with a high fidelity and a high entanglement. This scheme reduces the influence of the dissipation on the system evolution, has no requirement on the quality factors and reduces the experimental operation difficulty, which is proved to possess strong reliability and feasibility.