We investigate how the category of comodules of bimonads can be made into a monoidal category.It suffices that the monad and comonad in question are bimonads,with some extra compatibility relation.On a monoidal category of comodules of bimonads,we construct a braiding and get the necessary and sufficient conditions making it a braided monoidal category.As an application,we consider the category of comodules of corings and the category of entwined modules.