Diamond-based spin is one of the leading candidates for quantum computing, as it offers long coherence times, high-fidelity control, as well as low cooling requirements . A heterogeneously integrated photonic layer is required to connect individual diamond substrates which have limited qubits and small sizes, for large-scale and efficient computation . Here we demonstrate a design of the diamond nanobeam photonic crystal cavity on a sapphire waveguide layer that has a low optical loss for the visible wavelength region. The cavity is optimized for a high Q factor and thus a high Purcell factor to enhance a photon emission of the color centers.