  A space is nearly pseudocompact if and only if $\upsilon X\backslash X$ is
dense in $\beta X\backslash X$. If we denote $K=cl_{\beta X}(\upsilon
X\backslash X)$, then $\delta X=X\cup(\beta X\backslash K)$ is referred by
Henriksen and Rayburn \cite{hr80} as nearly pseudocompact extension of $X$.
Henriksen and Rayburn studied the nearly pseudocompact extension using
different properties of $\beta X$. In this paper our main motivation is to
construct nearly pseudocompact extension of $X$ independently and not using any
kind of extension property of $\beta X$. An alternative construction of $\beta
X$ is made by taking the family of all $z$-ultrafilters on $X$ and then
topologized in a suitable way. In this paper we also adopted the similar idea
of constructing the $\delta X$ from the scratch, taking the collection of all
$z$-ultrafilters on $X$ of some kind, called $hz$-ultrafilters, together with
fixed $z$-ultrafilter and then be topologized in the similar way what we do in
the construction of $\beta X.$ We have further shown that the extension $\delta
X$ is unique with respect to certain properties.
