  Dynamical Higgs mechanism on the light-front (LF) is studied using a (1+1)
dimensional model, with emphasis on the infrared divergence problem. The
consideration of the zero mode $ k^+ = 0 $ is not sufficient for investigating
dynamical symmetry breaking on the LF. It also needs to treat properly an
infrared divergence caused by internal momentum $ p^+ \to 0 ~ (p^+ \neq 0) $ in
the continuum limit. In order to avoid the divergence, we introduce an infrared
cutoff function $ F_{\rm IR} (p, \Lambda) $ which is not Lorentz invariant. It
is then shown that the gauge boson obtains mass dynamically on the LF.
