This paper is a comparative study of the impacts of different music genres (classical vs personal preferred) and timing settings to listen to the music on mental stress relief based on electroencephalogram (EEG). Fifty-six healthy young adults participated in this study, which involves a set of stress stimulus tasks and EEG recordings. Discrete Wavelet Transformation has been used to extract alpha wave from raw EEG data and then the widely used Frontal Alpha Asymmetry (FAA) was calculated to evaluate the stress state. Statistical results show that Frontal Alpha Asymmetry index obtained in classical music group has a significant difference if compared to personal preferred group and control group (rest in silence), indicating that classical music is a more effective tool for mental stress relief. Regarding the timing settings to listen to the music, there is not a statistical difference, indicating that listening to music before, during and after the stressful events has no significant relief effect.