We theoretically and numerically study current-induced modification of ferrimagnetic spin-wave dynamics when an electrical current generates adiabatic and nonadiabatic spin-transfer torques. We find that the sign of the Doppler shift depends on the spin-wave handedness because the sign of spin polarization carried by spin waves depends on the spin-wave handedness. It also depends on the sign of the adiabatic-torque coefficient, originating from unequal contributions from two sublattices. For a positive nonadiabaticity of spin current, the attenuation lengths of both right- and left-handed spin waves increase when electrons move in the same direction with spin-wave propagation. Our result establishes a way to simultaneously measure important material parameters of a ferrimagnet, such as angular momentum compensation point, spin polarization, and nonadiabaticity using current-induced control of ferrimagnetic spin-wave dynamics.