Based on neighborhood-based rough set model and covering-based rough set model, two matroidal structures which were matroid induced by neighborhood upper approximation number and matroid induced by covering upper approximation number were constructed. On one hand, two types of upper approximation number were defined through generalized rough set, and they were proven to satisfy rank function axiom in matroid theory, thus two types of matroids were obtained from the viewpoint of the rank function. On the other hand, some properties, such as independent sets, circuits, closures, closed sets, were proposed through rough set approach. Moreover, the concentions between upper approximation operators and closure operators were investigated. Futhuremore, the relationship between the covering and the matroid was studied. Result shows that elements and any union of them in covering are the closed sets of matroid induced by covering upper approximation number.