Two-dimensional　electromagnetic　particle-in-cell　simulations　are　performed　to　investigate　the　transport　of　relativistic　electron　beams　co-moved　with　a　proton　beam　in　background　plasmas.　For　the　beam　with　the　radius　much　larger　than　the　plasma　skin　depth,　the　current　filamentation　instability　excited　by　the　relativistic　electron　beam　can　be　clearly　observed　and　the　transverse　magnetic　fields　in　the　plasma　increase　significantly.　The　proton　beam　is　modulated　strongly　by　the　electromagnetic　fields　in　plasmas,　and　a　netlike　structure　in　the　beam　profile　is　formed　with　a　high　density　contrast,　which　can　be　provided　as　an　effective　tool　to　diagnose　the　instability.　The　dynamic　effects　of　plasma　ions　are　shown　to　be　important　and　play　a　significant　role　in　the　dynamic　evolution　of　the　proton　beam.　©　2018　Author(s).