In previous works, psychoacoustic parameters have been used for objective quantification. However, these parameters do not agree well with subjective assessment. Therefore, the correlation between psychoacoustic parameters and the subjective rating of door closing sounds of sampled cars is low, and it is not sufficient to use psychoacoustic parameters as an objective metric to quantify the sound quality of door closing sounds. In this paper, a new method is proposed to objectively quantify the sound quality based on physiological acoustics and statistical signal processing. The gammatone filter, as a pre-processing, is used in models of the auditory system and kurtosis, which is the fourth-order moment of temporal signal, and is used to extract information about sound quality quantification for door closing sounds. The new metric obtained through the proposed method is highly correlated with subjective rating, and it is successfully applied to the quantification of the sound quality of door closing sounds.