In linear regression under heteroscedastic variances, Aitken estimator is employed to account for the differences in variances. Employing the same principle, we propose the Nadaraya-Watson regression estimator with variable variance-stabilizing bandwidth (VS bandwidth) that minimizes asymptotic MISE (AMISE) while maintaining asymptotic homoscedasticity. We examine its local and global properties relative to the MISE minimizing fixed bandwidth. The proposed VS bandwidth produces the asymptotic variance smaller on some part of the support than the fixed bandwidth and may in some cases achieve smaller AMISE than its fixed counterpart. In numerical examples, we find that the proposed VS bandwidth is more serviceable when the distribution of X’s are flatter.