Hearing aids are commonly used to overcome impairment associated with hearing loss. Recent surveys have shown that hearing aid users are often dissatisfied with the speech quality. However, only subjective methods (e.g., questionnaires) are used to assess speech quality, and the objective methods used to verify the performance of hearing aids have major limitations. This study proposes an objective method called variations of dynamic range (VDR) score for assessing hearing aid speech quality. The method uses quantitative differences between spectra for aided and unaided speech based on Speechmap. Two experiments were performed in this study: (1) one to verify the correlation between scores for the perceptual evaluation of speech quality (PESQ) and VDR in assessing speech quality produced under three compression ratios (CR) of wide-dynamic-range amplification in one channel, and (2) one to verify that the VDR score is consistent with results from clinical trials in the literature. The experiments involved hearing aids fitted using desired sensation level [input/output] (DSL [i/o]) and adaptive dynamic range optimization (ADRO), and stimulated by speech sounds at moderate and loud levels. The VDR scores were measured using the Audioscan Verifit hearing aid fitting system to assess the speech quality of hearing aids. The results indicate that PESQ scores were 3.56, 2.25, and 1.98, and VDR scores were 2.5, 29, and 36 dB for CRs of 1.0, 2.0, and 4.0, respectively. The VDR and PESQ methods provided similar assessments of speech quality produced by hearing aids fitted for flat mild hearing loss (high and low PESQ and VDR scores, respectively, indicate good speech quality). In addition, the average VDR scores were significantly lower (p < 0.05) for hearing aids fitted using ADRO than those for hearing aids fitted using DSL [i/o]. The VDR scores are consistent with PESQ scores for hearing aids with different prescriptions, and are consistent with clinical reports that found the speech quality for hearing aids fitted using ADRO to be higher than that obtained using DSL [i/o]. These results indicate the potential of the VDR score for accurately assessing the speech quality of hearing aids.