High Efficiency Video Coding (HEVC) enables significantly improved compression performance relative to existing standards. However, the advance also requires high computational complexity. To accelerate the intra prediction mode decision, a minimum risk Bayesian classification framework is introduced. The classifier selects a small number of candidate modes to be evaluated by a rate-distortion optimization process using the sum of absolute Hadamard transformed difference (SATD). Moreover, the proposed method provides a loss factor that is a good trade-off model between computational complexity and coding efficiency. Experimental results show that the proposed method achieves a 31.54% average reduction in the encoding run time with a negligible coding loss of 0.93% BD-rate relative to HEVC test model 16.6 for the Intra_Main common test condition.