  In this article we develop the theory of $H$-Orlicz space generated by
generalised Young function. Modular convergence of $H$-Orlicz space for the
case of vector-valued functions and norm convergence in $\mcH^\theta(X,
\bar{\mu})$ where $X$ is any Banach space are discussed. Relationships of
modular convergence and norm convergence of $H$-Orlicz spaces are discussed.
