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A minimum generation error (MGE) criterion had been proposed to solve the issues related to maximum likelihood (ML) based HMM training in HMM-based speech synthesis. In this paper, we improve the MGE criterion by imposing a log spectral distortion (LSD) instead of the Euclidean distance to define the generation error between the original and generated line spectral pair (LSP) coefficients. Moreover, we investigate the effect of different sampling strategies to calculate the integration of the LSD function. From the experimental results, using the LSDs calculated by sampling at LSPs achieved the best performance, and the quality of synthesized speech after the MGE-LSD training was improved over the original MGE training.