  A U(3) family gauge boson model is investigated based on
U(3)$\times$[U(1)]$^3$ gauge symmetry. In this model, of nine U(3) family gauge
bosons $A_i^{\ j}$, those with $i=j$ are considerable heavy compared with those
with $i \neq j$, so that the model can be released from severe constraints due
to the observed $K^0$-$\bar{K}^0$ mixing, and so on. We speculate that the
lightest gauge boson is $A_2^{\ 3}$ and its mass is of $2 - 6$ TeV. Thereby,
visible effects of the family gauge bosons are discussed. Especially, an
observation of $\mu^- +N \rightarrow e^- + N$ versus no observation of $\mu
\rightarrow e +\gamma$ will be a promising test for the present scenario.
