The new High Efficiency Video Coding (HEVC) standard is achieving higher encoding efficiency when compared to its predecessors such as H.264/AVC. One of the factors responsible to this improvement is the intra prediction method, which introduces a larger number of prediction directions resulting in an enhanced rate-distortion (RD) performance at the cost of a higher computational complexity. This paper proposes an algorithm to accelerate the intra mode decision, reducing the complexity of intra coding. The acceleration procedure takes into account the edge direction information and explores the correlation of intra modes across levels of the HEVC hierarchical tree structure. Experimental results show that the proposed algorithm provides a decrease of up to 40.82% in the HEVC intra prediction processing time, with a small degradation in encoding efficiency (BD-PSNR loss of 0.1 dB on average).