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A new algorithm for adaptive filters, named variable exponent nonlinearly processed correlation algorithm (VE-NPCA), is proposed and studied. The exponent, r, in the "rth power function" of the correlation between the error and the filter input is adaptively controlled by an estimate of the error power. The variable exponent achieves a significant improvement in the convergence rate of the sign-sign algorithm that is known to be highly robust against disturbances but considerably slow in convergence. The results of simulations for some examples prove the effectiveness of the proposed VE-NPCA. Analysis yields a set of difference equations for calculating the theoretical convergence curves which appear to be in good agreement with the simulated ones.