  We give an extension of Hua's inequality in pre-Hilbert $C^*$-modules without
using convexity or the classical Hua's inequality. As a consequence, some known
and new generalizations of this inequality are deduced. Providing a Jensen
inequality in the content of Hilbert $C^*$-modules, another extension of Hua's
inequality is obtained. We also present an operator Hua's inequality, which is
equivalent to operator convexity of given continuous real function.
