  In this paper, we show that harmonic Bloch mappings are Lipschitz continuous
with respect to the pseudo-hyperbolic metric. This result improves the
corresponding result of Theorem 1 of [P. Ghatage, J. Yan, and D. Zheng,
Composition operators with closed range on the Bloch space, Proc. Amer. Math.
Soc. 129 (2000), 2039-2044]. Furthermore, we prove the similar property for
harmonic quasiregular Bloch-type mappings.
