The invention relates to a method for boiling high concentration pulping in normal pressure or low pressure by an alkaline method with zero residual alkaline, and the method comprises adding accelerating agent in the boiling process and utilizing a double screw to rub and squeeze a pulper, leading pulp making and boiling process with an alkaline method to go on in normal pressure or low pressure, and leaving no residual alkaline in black liquor, leading pulp to always keep a higher density in the pulping process of boiling, washing and bleaching, and the pulp which is prepared can meets the requirement of paper making. Accelerating agent chooses one or a plurality of magnesium hydrate, potassium hydrate, sodium metasilicate, sodium sulfide, sodium sulfite, ammonium sulfite and carbamide. Special-purpose pulping boiling equipment and high-pressure boilers are not needed by pulping paper mills through utilizing the invention, in the process of pulping, pulp always keeps higher density, and black liquid has high density, little numbers and low energy consumption, alkaline recovery project with great investment is not needed to be built, and the invention enables black liquid to prepare fertilizer or other chemical products with high quality, and the invention is suitable for popularizing and applying.