Maleic　anhydride-grafted　carbon　fiber　(CF-g-MAH)　was　prepared　by　a　solid-phase　grafting　method.　The　rheological　behavior,　morphology,　mechanical　properties,　and　nonisothermal　crystallization　behavior　of　pure　poly(ethylene　terephthalate)　(PET)　and　PET/CF　and　PET/CF-g-MAH　composites　were　investigated.　The　rheological　analyses　and　mechanical　tests　show　that　the　addition　of　CF　or　CF-g-MAH　increased　the　complex　viscosity　and　mechanical　properties　of　PET.　The　morphology　observations　confirm　that　the　introduction　of　the　MAH　group　on　the　surfaces　of　the　CF　enhanced　the　interactions　between　the　CF　and　PET,　resulting　in　the　fine　dispersion　of　CF-g-MAH　in　the　PET　matrix.　In　addition,　the　analyses　of　the　nonisothermal　crystallization　behavior　of　pure　PET　and　the　PET/CF　and　PET/CF-g-MAH　composites　show　that　CF　or　CF-g-MAH　can　act　as　a　heterogeneous　nucleating　agent　in　PET　and　accelerate　its　crystallization.　Compared　to　CF,　CF-g-MAH　is　a　more　effective　nucleator　for　PET.　©　The　Author(s)　2018.