We propose a dual to variance ratio-type estimator to estimate the finite population variance. The optimum mean square error of this estimator is equal to variance of a linear regression estimator and is better than the usual unbiased variance estimator and Isaki (Jour Amer. Statis Assoc. 78: 117-123, 1983) estimator. We use the jackknife technique to make the proposed estimator unbiased. The validity of the proposed estimator is examined by using the various data sets.