  In this paper we study the complete invariant metrics on Cartan-Hartogs
domains which are the special types of Hua domains. Firstly, we introduce a
class of new complete invariant metrics on these domains, and prove that these
metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures
under these new metrics are bounded from above and below by the negative
constants. Thirdly, we estimate the holomorphic sectional curvatures of the new
metrics, we prove that the holomorphic sectional curvatures are bounded from
above and below by the negative constants. Finally, by using these new metrics
and Yau's Schwarz lemma we prove that the Bergman metric is equivalent to the
Einstein-K\"ahler metric. That means the Yau's conjecture is true on
Cartan-Hartogs domain.
