  We use the redshift Hubble parameter $H(z)$ data derived from relative galaxy
ages, distant type Ia supernovae (SNe Ia), the Baryonic Acoustic Oscillation
(BAO) peak, and the Cosmic Microwave Background (CMB) shift parameter data, to
constrain cosmological parameters in the Undulant Universe. We marginalize the
likelihood functions over $h$ by integrating the probability density $P\propto
e^{-\chi^2/2}$. By using the Markov Chain Monte Carlo (MCMC) technique, we
obtain the best fitting results and give the confidence regions on the
$b-\Omega_{\rm m0}$ plane. Then we compare their constraints. Our results show
that the $H(z)$ data play a similar role with the SNe Ia data in cosmological
study. By presenting the independent and joint constraints, we find that the
BAO and CMB data play very important roles in breaking the degeneracy compared
with the $H(z)$ and SNe Ia data alone. Combined with the BAO or CMB data, one
can improve the constraints remarkably. The SNe Ia data sets constrain
$\Omega_{\rm m0}$ much tighter than the $H(z)$ data sets, but the $H(z)$ data
sets constrain $b$ much tighter than the SNe Ia data sets. All these results
show that the Undulant Universe approaches the $\Lambda \rm$CDM model. We
expect more $H(z)$ data to constrain cosmological parameters in future.
