It is known that the standard lattice Boltzmann method has near-vacuum limit,
i.e., when the density is near zero, this method is invalid. In this letter,
we propose a simple lattice Boltzmann model for one-dimensional flows. It
posesses the ability of simulating near-vaccum area by setting a limitation on
the relaxation factor. Thus, the model overcomes the disadvantage of
non-physical pressure and density. The numerical examples show its results
are satisfactory.