  In a warped 6D world with an extra 2-dimensional sphere, we propose an
exactly solvable model for fermion masses with zero mode. The warp factor is
given by $\phi (\theta ,\varphi )=\sin{\theta }\cos{\varphi }$, which is a
solution to the 6D Einstein equation with the bulk cosmological constant
$\Lambda $ and the energy-momentum tensor of the bulk matter fields. Our model
provides another possibility of obtaining fermion zero mode, rather than
traditional model based on Dirac's monopole.
