  We propose a new model with flavor-dependent gauged $U(1)_{B-L_1}\times
U(1)_{B-L_{2}-L_{3}}$ symmetry in addition to the flavor-blind one in the
standard model. The model contains three right-handed neutrinos to cancel gauge
anomalies and several Higgses to construct the measured fermion masses. We show
the generic feature of the model and explore its phenomenology. In particular,
we discuss the current bounds on the extra gauge bosons from the K and B meson
mixings as well as the LEP and LHC data and focus on their contributions to the
lepton flavor violating processes of $\ell_{i+1}\to \ell_i\gamma$ (i=1,2).
