In system identification, the selection of the optimum taplength of an adaptive filter is desirable to balance the conflicting requirements of computational cost and the steady-state performance. The performance of the original fractional tap-length least-mean-square LMS (FT-LMS) algorithm is severely degraded with a change in the variance of the input excitation signal, as well as with a change in the variance of the tap-coefficients of the unknown system. In this paper, a normalized LMS style variable tap-length (VTL) algorithm is proposed. The main idea is to efficiently normalize the step-size in the update equation for the tap-length. Furthermore, the idea of fractional gradient is incorporated with the weight-update equation of the adaptive filter. Extensive computer simulations are carried out, which demonstrate that the proposed algorithm gives robust performance in the time-varying environment.