We propose a scheme to realize strong photon antibunching with lower photon nonlinearity in a photonic molecule consisting of two photonic cavities, one of which contains a quantum dot (QD). This strong photon antibunching is attributed to destructive quantum interference effect which suppresses the two-photon excitation of the cavity field. That g2(0) ≈10-4 can be achieved with modest QD-cavity coupling strength g = 1.1κ and cavity tunneling strength J = 3κ when the system is driven by single laser field. To further reduce the requisite tunneling and make the system tunable, two laser fields are applied to the system. The strong photon antibunching (g2(0) ≈10-3) can be achieved with a relatively large intracavity photon number by optimizing the phase between two driving laser fields when J = 0.9κ . Moreover, the system shows a strong robustness of maintaining strong photon antibunching within a large parameter variation under the optimal phase condition. Our scheme provides a flexible and efficient method for solid state quantum single photon sources.