The introduction of a larger number of prediction directions in HEVC intra coding process intended to achieve higher encoding efficiency when compared to its predecessors such as H.264/AVC. However, this increase in the number of prediction directions resulted in an enhanced rate-distortion (RD) performance at the cost of very high computational complexity. This paper proposes an algorithm to accelerate the intra coding mode decision, reducing the computational complexity of this process. The acceleration procedure takes into account the edge orientation of the current PU texture and the correlation between the intra modes chosen across the levels of the HEVC tree coding structure. Experimental results show that the proposed algorithm provides a decrease of up to 37.85% in the HEVC intra prediction processing time, with a small degradation in encoding efficiency (BD-PSNR loss of 0.06 dB on average).