We introduce the concept of $D_{w,p}$-classical orthogonal polynomials, where $D_{w,p}$ is the lowering operator given by $D_{w,p}:=\frac{\tau_{-w}-\tau_{-p}}{w-p}$, $w, p\in\mathbb{C}$, with $\tau_{-w}f(x):=f(x+w)$. We conclude that these polynomials are the shifted discrete classical orthogonal polynomials.