  An accelerating flat universe with a variable cosmological term is obtained
in the Robertson-Walker metric. The variable cosmological term is defined by
the correction terms of the metric tensor field. Simple solutions of the scale
factor and the cosmological term are shown. In this model of the universe, the
magnitude-redshift relation is analytically studied to see if the model
reproduces the tendency of the present observational data. The equation of
state parameter $\gamma$ is touched.
