  Assuming the Majorana nature of massive neutrinos, we generalize the
Friedberg-Lee neutrino mass model to include CP violation in the neutrino mass
matrix M_\nu. The most general case with all the free parameters of M_\nu being
complex is discussed. We show that a favorable neutrino mixing pattern (with
\theta_12 \approx 35.3^\circ, \theta_23=45^\circ, \theta_13 \neq 0^\circ and
\delta=90^\circ) can naturally be derived from M_\nu, if it has an approximate
or softly-broken \mu-\tau symmetry. We also point out a different way to obtain
the nearly tri-bimaximal neutrino mixing pattern with \delta=0^\circ and
non-vanishing Majorana phases.
