In the present paper we define multiplier double sequence spaces $\chi_M^2[\hat{c},\Delta^m,u,p,q]$ and $\Lambda_M^2[\hat{c},\Delta^m,u,p,q]$ by using a sequence of Orlicz functions $M = (M_{mn})$ and a multiplier function $u = (u_{mn})$. We also make an effort to study some topological properties and inclusion relations between these spaces.