In this paper, we introduce and study the notion of weighted slant Hankel operator $K^\beta_\phi$, $\phi \in L^\infty (\beta)$ on the space $L^2(\beta)$, $\beta=\{\beta_n\}_{n \in \Bbb{Z}}$ being a sequence of positive numbers with $\beta_0=1$. In addition to some algebraic properties, the commutant and the compactness of these operators are discussed.