The invention provides a novel topological-structure multifunctional single-phase grid-connected inversion system and method. The system comprises a photovoltaic direct-current power source, a first capacitor, a second capacitor, a photovoltaic panel end capacitor, a switching tube parallel capacitor, a first inductor, a coupling inductance primary-side self-inductor, a coupling inductance secondary-side self-inductor, a coupling inductance mutual inductor, a diode, a first switching tube, a second switching tube and a single-phase alternating-current power distribution network. According to the system, an inductance value of the coupling inductance primary-side self-inductor and an inductance value of the coupling inductance mutual inductor are equal, so that switching ripples of a grid-connected current are eliminated; and since a cathode of the photovoltaic direct-current power source, a cathode of the photovoltaic panel end capacitor, a cathode of the switching tube parallel capacitor, a source of the first switching tube and a cathode of the second capacitor are connected with a neutral line of the alternating-current power distribution network, a common-mode leakage current is eliminated. According to the method, decoupling of photovoltaic cell panel output power and alternating-current-side grid-connected power can be realized just by regulating switching frequency, andpower fluctuation of doubled grid frequency at a direct-current side can be effectively suppressed.