In this paper, we study an objective quality measure that approximates the subjective mean opinion score (MOS) for bandwidth-extended wideband speech with respect to narrowband speech. Bandwidth-extended speech should be widely evaluated by a subjective quality assessment such as MOS. However, such subjective quality assessments are expensive and time-consuming. This paper proposes a new objective quality measure that combines the perceptual evaluation of speech quality (PESQ) and spectral-distortion. We evaluated the correlation between our proposed scheme and MOS using AMR and AMR-WB speech codecs. The coefficient of correlation between the proposed scheme and the MOS value was found to be 0.973. We concluded that the proposed scheme is a valid and effective objective quality measure.