We theoretically demonstrate microwave-induced dynamical switching of magnetic topology in centrosymmetric itinerant magnets by taking the Kondo-lattice model on a triangular lattice, which is known to exhibit two types of skyrmion lattices with different magnetic topological charges of |N sk |=1 and |N sk |=2. Our numerical simulations reveal that intense excitation of a resonance mode with circularly polarized microwave field can switch the magnetic topology, i.e., from the skyrmion lattice with |N sk |=1 to another skyrmion lattice with |N sk |=2 or to a nontopological magnetic order with |N sk |=0 depending on the microwave frequency. This magnetic-topology switching shows various distinct behaviors, that is, deterministic irreversible switching, probabilistic irreversible switching, and temporally random fluctuation depending on the microwave frequency and the strength of external magnetic field, variety of which is attributable to different energy landscapes in the dynamical regime. The obtained results are also discussed in the light of time-evolution equations based on an effective model derived using perturbation expansions.