With the characteristics of ultrasmall, ultrafast, and topological protection, optical skyrmions are great prospects for applications in high intensity data stroage, high resolution microscopic imaging, and polarization sensing. Flexible control over the topology of optical skyrmions is required for practical implementation/application. At present, the manipulation of optical skyrmions usually relies upon the change of spatial structure, which results in a limited-tuning range and a discontinuous control in the parameter space. Here, we propose continuous manipulation of the graphene plasmon skyrmions based on the electrotunable properties of graphene. By changing the Fermi energy of one pair of the standing waves or the phase of incident light, one can achieve topological state transformation of graphene plasmon skyrmions, which is evident by the change of skyrmion number from 1 to 0.5. The direct manipulation of the graphene plasmon skyrmions is demonstrated by simulation results based on the finite element method. Our work suggests a feasible way to flexibly control the topology of an optical skyrmionic field, which can be used for novel integrated photonic devices in the future.