  The sub-barrier fusion excitation functions are measured for the first time
for the system $^7$Li +$^{28}$Si by the characteristic $\gamma$-ray method in
the energy range $E_{lab}$= 7-11.5 MeV. The results show an enhancement, below
the barrier, by about a factor of two when compared with the one-dimensional
barrier penetration (1D BPM) model. Introduction of coupling with the
rotational 2$^{+}$ state (1.779MeV) of the target improves the fit somewhat,
but still an enhancement of about 25-40% remains.
