  In this paper, we discuss some properties on hyperbolic-harmonic mappings in
the unit ball of $\mathbb{C}^{n}$. First, we investigate the relationship
between the weighted Lipschitz functions and the hyperbolic-harmonic Bloch
spaces. Then we establish the Schwarz-Pick type theorem for hyperbolic-harmonic
mappings and apply it to prove the existence of Landau-Bloch constant for
mappings in $\alpha$-Bloch spaces.
