As a biconical interference model is constructed to design a double-period graded photonic crystal (GPC) structure, we design a GPC lens with graded dielectric column size based on the graded light intensity distribution of the GPC structure, and study the influence of the inner and outer cone interference angle on the GPC period and the focusing characteristics of the lens. It is found that the sine difference of the inner and outer cone angles of the interference beam determines the large period of the lens, while the outer cone angle directly affects the small period. When the large period of the lens is fixed, the smaller the small period is, the better the focusing effect will be. What’s more, when the small period is fixed, the smaller the large period is, the larger the numerical aperture of the lens will be. The designed lens can achieve sub-diffraction-limit focusing. This research is helpful for the application of lenses in optical coupling, optical integration, optical display, and imaging.