The invention discloses a process for comprehensive recovery of copper-cobalt-containing sulfuric acid slag. The process comprises the following steps that (1) the copper-cobalt-containing sulfuric acid slag is subjected to bioleaching, a vaccinal bacterium is Sulfobacillus thermosulfiooxidans 6Y-1, the leaching pH value is maintained within 1.8-2.5, the reaction period is 1.5-3 h, and the temperature is 60-80 DEG C; (2) bioleaching liquid is subjected to extraction through a copper extractant, an extraction phase enters electrodeposition after reverse extraction through sulfuric acid, and finally cathode copper is obtained; (3) copper extraction residual liquid is precipitated through limestone, iron is removed, cobalt extraction is conducted on a solution after iron removing through a mixed extractant of P507 and Cyanax272, the extraction phase is subjected to reverse extraction through sulfuric acid and concentrated, and a cobalt product is obtained; and (4) bioleaching slag obtained from the step (1) and iron slag obtained after precipitating and iron removing from the step (3) are combined and subjected to reduction roasting, and a metallization pellet is obtained. Valuable metal in the sulfuric acid slag is recycled through bioleaching firstly, meanwhile, the iron grade of the leaching slag is improved, the sulphur grade in the leaching slag is reduced, the quality of a subsequent metallization pellet is further improved, and finally comprehensive recovery of copper-cobalt iron is realized.