Proximity to functional substrates may enhance the coupling between the quantum degrees of freedom and thus develop nontrivial quantum effects in graphene. Here, we demonstrate the successful fabrication of graphene in proximity to atomically flat magnetic insulating LaMnO3 films. The insulating nature of the LaMnO3 films not only ensures the electronic transport only occur in the graphene layers but also allow them to serve as dielectric layers for gating. Transport measurements reveal anomalous behaviors, including asymmetrical longitudinal magnetoresistivity and nonlinear Hall effect. This work may pave a way toward the realization of intriguing quantum phases in graphene.