In this paper, a novel hybrid cubemap projection (HCP) is proposed to improve the 360-degree video coding efficiency. HCP allows adaptive sampling adjustments in the horizontal and vertical directions within each cube face. HCP parameters of each cube face can be adjusted based on the input 360-degree video content characteristics for a better sampling efficiency. The HCP parameters can be updated periodically to adapt to temporal content variation. An efficient HCP parameter estimation algorithm is proposed to reduce the computational complexity of parameter estimation. Experimental results demonstrate that HCP format achieves on average luma (Y) BD-rate reduction of 11.51%, 8.0%, and 0.54% compared to equirectangular projection format, cubemap projection format, and adjusted cubemap projection format, respectively, in terms of end-to-end WS-PSNR.