Let R be a ring, 1 R be the identity of ring R and N be an R-module on R. In this work, we are going to give a new definition that it is called an action of R-module groupoids. First, we are going to give the definition of the action of the R-module groupoids on the R-module N. Then we obtained a new category RMGpdOp(Ω) of actions of Ω on R-modules. We also find that there is a groupoid Ω ▷◁ N on N. Ω ▷◁ N is called action R-module groupoid. Finally, we prove that the category RMGpdOp(Ω) of actions of R-module groupoids is equivalent to RMGpdCov(Ω) of coverings of R-module groupoids.