The invention discloses a hypo-peritectic steel slab continuous casting method, which is applied to the technical field of steelmaking and continuous casting. A continuous casting process of the method comprises the steps of injecting molten steel into a tundish, and distributing the molten steel into various crystallizers through a nozzle of the tundish; and after distributing the molten steel into the various crystallizers through the nozzle of the tundish, putting crystallizer casting powder with the alkalinity being 1.75+/-0.10 onto molten steel surfaces in the crystallizers, wherein the crystallizer casting powder is prepared from the component in percentage by mass: 0.6 to 3.0 percent of Li2O. During the process of solidifying the molten steel in the crystallizers, the crystallizersare non-sinusoidally vibrated through a vibration device, so that the crystallizer casting powder can be ensured to guarantee lubrication between solidified slab shells and walls of the crystallizersunder the condition of high alkalinity, longitudinal surface cracks of a slab are reduced, meanwhile, the crystallizers cannot be adhered, and the slab surface quality is improved.