A non-saponification method for extraction separation of nickel and cobalt is provided. The method includes subjecting nickel- and cobalt-containing solid waste to high-temperature calcination, performing acid leaching to form an acid leachate, mixing synergistic extractants and a diluting agent, reacting the mixture with the acid leachate, and extracting the cobalt in the acid leachate to achievenickel-cobalt separation. No NaOH adopted as a saponifier is used in the method, thus avoiding excessive emission of saponification waste water. An acidic extractant B326 and an alkaline extractant methyl chloride N204 are synergistic under acidic conditions and the cobalt in the acid leachate is extracted into an organic phase effectively, thus achieving nickel-cobalt separation. For power battery solid waste the discharging amount of which is huge because power batteries are widely applied, the method is simple to operate and low in equipment requirements and has huge industrial practicality.