  The width of the decay $\tau\rightarrow f_1 \pi \nu_\tau$ has recently been
measured by the BaBar experiment. The estimation of this width is given in the
framework of the NJL model with the axial-vector mesons. Prediction is in
agreement with the experimental data. It is shown that the $\pi-a_1$ transition
contribution plays an important role and allows us to bring the NJL prediction
to the data.
