Summary: Given two real numbers \(a\) and \(b\) where \(a<b\). Let \(\delta\) be a nonnegative real function on interval \([a,b]\). By changing the role of interval system on \(\mathbb{R}\) by \(\delta\)-fundamental interval system, we construct the \(\delta\)-Henstock integral \((R^*_\delta\)-integral) of real function on \([a,b]\). We discuss some properties of the integral. Furthermore, we also discuss the equivalence of \(R^*_\delta\)-integral to \(\delta\)-special Denjoy integral \((D^*_\delta\)-integral).