Photon's effective mass is an important parameter of an optical cavity mode, which determines the strength of light-matter interaction. Here, we propose a novel method for controlling the photon's effective mass by using coupled photonic cavities and designing the angular dependence of the coupling strength. This can be implemented by employing a high-contrast grating (HCG) as the coupling reflector in a system of two coupled vertical cavities, and engineering both the HCG reflection phase and amplitude response. Several examples of HCG-based coupled cavities with novel features are discussed, including a case capable of dynamically controlling the photon's effective mass to a large extent while keeping the resonance frequency same. We believe that full-control and dynamical-tuning of the photon's effective mass may enable new possibilities for cavity quantum electrodynamics studies or conventional/polariton laser applications. For instance, one can dynamically control the condensate formation in polariton lasers by modifying the polariton mass.