Full-waveform inversion (FWI) is one of the core technologies developed in exploration geophysics. Through FWI, the subsurface velocity structures can be constructed and the attenuation parameter (the quality factorQ) model can be inverted, which is helpful to characterize the types and structures of subsurface media (such as the fluid and collapse column in collapse column). This is significant for the exploration and development of natural resources such as coal, oil and gas. Parameter crosstalk is the key difficulty of visco-elastic FWI. Due to the influences of velocity errors, the inverted Q models contain very strong crosstalk noise. To solve this problem, the visco-elastic FWI theory and method based on multi-objective function was proposed. Specifically, the velocity structures are inverted using the travel time, and the Q models are inverted with the central-frequency objective function. Then, the velocity and Q models are inverted simultaneously with the waveform difference objective function. As the central-frequency is mainly influenced by attenuation, the influences of velocity error on Q model inversion could be effectively reduced. Finally, the algorithm was verified by numerical simulation for its capability to invert the velocity and Q models effectively.