Abstract: Two asymmetric cost function for whispered speech enhancement methods are proposed. The cost of the amplification distortion and the attenuation distortion are different in both methods. The Modified Itakura-Saito (MIS) distance function gives more penalties to speech amplification distortion while the Kullback-Leibler (KL) divergence function gives more penalties to speech attenuation distortion. The experimental results show that the MIS method gains larger intelligibility improvement of the whispered speech than the conventional speech enhancement algorithms in much lower Signal to Noise Ratio (SNR) less than -6 dB, and the KL method has similar intelligibility improvement performance to the Minimum Mean Square Error (MMSE) speech enhancement method. The results confirm that the amplification distortion and the attenuation distortion have different effects on the intelligibility of the enhanced whisper. Specifically, larger attenuation distortion can improve speech intelligibility in lower SNR condition and it has a little influence on speech intelligibility in high SNR condition.