We present a novel broken-nanoring, which can realize strongly localized confinement and highly enhancement for both electric and magnetic fields at two resonant modes excited by normal incident azimuthally polarized light. Two resonant modes of the broken-nanoring are formed by different resonant mechanisms as different resonant lengths. The physical model for two resonant modes is also proposed to explain the mechanisms of the electromagnetic enhancement. The enhancement of the electric and magnetic fields can be further improved by adding a nanoring at the outside of the broken-nanoring to form a composite nanoring, which can freely tune or easily merge the resonant modes of the solitary broken-nanoring while keeping larger enhancement of the electric and magnetic fields.