  We calculate the Sivers function of $\bar{u}$ and $\bar{d}$ quarks using the
overlap representation within the light-cone formalism. The light-cone wave
functions of the proton is obtained in terms of the $|\bar{q} q B\rangle$ Fock
states motivated by the meson-baryon fluctuation model. We consider the
final-state interaction at the level of one gluon exchange. In a simplified
scenario, the Sivers function of $\bar{u}$ and $\bar{d}$ can be expressed as
the convolution of the Sivers function of the pion inside the proton and the
unpolarized distribution of $\bar{q}$ inside the pion. The model parameters are
fixed by fitting the unpolarized sea quark distributions to the known
parameterizations. We present the numerical results for $f_1^{\perp
\bar{u}/p}(x,\boldsymbol{k}_T^2)$ and $f_1^{\perp
\bar{d}/p}(x,\boldsymbol{k}_T^2)$. The first transverse moment of the sea quark
Sivers functions in our model are find to be negative and the magnitude is
about 0.004 at most.
