Recent advances in display, networking, and computing technologies have resulted in changing industry focus towards 360-degree/omnidirectional images as witnessed by increased interest in virtual reality (VR) and augmented reality (AR). Numerous curves are generated for 360-degree images due to the lens curvature and projection format. However, in High Efficiency Video Coding (HEVC), the conventional angular intra modes cannot handle them well since only straight lines can be predicted. More enhanced 360-degree image coding is essential for higher efficiency of storage and transmission. Therefore, we propose a new coding mode, called 360-degree intra mode, for predicting the coding units with curves. Experimental results show that our 360-degree intra mode improves the coding efficiency of HEVC by 0.32% on average and up to 0.74% Bj⊘ntegaard delta bit rate reduction.