Levels in the neutron-rich 104Mo nucleus have been investigated by observing prompt γ-rays from the spontaneous fission of 252Cf with the Gammasphere detector array. The ground-state band, the one-phonon and the twophonon γ-vibrational bands as well as a quasiparticle band have been confirmed and expanded with spin up to 14h. Other two side bands probably built on new quasiparticle states are identified. The possible configurations for the quasiparticle bands are discussed. Two of the quasiparticle bands show larger moments of inertia and may have pair-free characteristics. The levels of the ground-state band, the one-phonon γ-band and the two-phonon γ-band calculated from a general collective model are in close agreement with the experimental data.