  We study in this paper chameleon cosmology applied to
Friedmann-Robertson-Walker space, which gives rise to the equation of state
(EoS) parameter larger than -1 in the past and less than -1 today, satisfying
current observations. We also study cosmological constraints on the model using
the time evolution of the cosmological redshift of distant sources which
directly probes the expansion history of the universe. Due to the evolution of
the universe's expansion rate, the model independent Cosmological Redshift
Drift (CRD)test is expected to experience a small, systematic drift as a
function of time. The model is supported by the observational data obtained
from the test.
