  We investigate a matter dominated navigation cosmological model. The
influence of a possible drift (wind) in the navigation cosmological model makes
the spacetime geometry change from Riemannian to Finslerian. The evolution of
the Finslerian Universe is governed by the same gravitational field equation
with the familiar Friedmann-Robertson-Walker one. However, the change of space
geometry from Riemannian to Finslerian supplies us a new relation between the
luminosity distant and redshift. It is shown that the Hubble diagram based on
this new relation could account for the observations on distant Type Ia
supernovae.
