  Since it can describe the rotation curves of galaxies without dark matter and
can give rise to accelerated expansion, conformal gravity attracts much
attention recently. As a theory of modified gravity, it is important to test
conformal gravity with astrophysical observations. Here we constrain conformal
gravity with SNIa and Hubble parameter data and investigate whether it suffers
from an age problem with the age of APM~08279+5255. We find conformal gravity
can accommodate the age of APM~08279+5255 at 3 $\sigma$ deviation, unlike most
of dark energy models which suffer from an age problem.
