We investigated the electric-current-induced dynamics of bubble domains in a perpendicularly magnetized ferrimagnetic {Tb/Co}7 multilayer wire with a heavy-metal Pt cap layer. The {Tb/Co}7 wire with the transition-metal-dominant and rare-earth-dominant magnetizations was obtained by changing temperature. We found that the bubble domains moved to the electric current direction with growing in oblique angles when electric current pulses were applied. The oblique directions of the bubble-domain’s growth in the {Tb/Co}7 wire with the transition-metal-dominant and rare-earth-dominant magnetizations were opposite with each other. The micromagnetic simulations imply that these oblique growths are accounted by the spin injection from the Pt layer via the spin Hall effect.