Intrinsic mode coupling in a graded-index plastic optical fiber (GI POF) is investigated using the developed coupled power theory for a GI POF with a microscopic heterogeneous core. The results showed that the intrinsic material properties can induce random power transitions between all the guided modes, whereas the structural deformation of microbending results in nearest-neighbor coupling. It was numerically demonstrated that efficient group-delay averaging due to intrinsic mode coupling brings the pronounced bandwidth enhancement in fibers with much shorter length than the case of glass multimode fibers.