The invention belongs to the technical field of recovery of lithium-ion batteries and particularly relates to a method for recovering a waste/used lithium iron phosphate positive-pole material by an acid leaching method. The method provided by the invention comprises the following steps: (a) carrying out acid leaching: adding acid into the lithium iron phosphate positive-pole material for acid leaching so as to obtain a suspension, and carrying out filtration, so as to obtain filtrate; (b) carrying out oxidation: adjusting the pH value of the filtrate obtained in the step (a) to be smaller than 1, and adding an oxidant into the filtrate to oxidate ferrous ions in the filtrate into ferric ions, so as to obtain a mixed solution; (c) carrying out separation: adjusting the pH value of the mixed solution obtained in the step (b) to be 1.5 to 4, carrying out a reaction for 1 to 3 hours at the temperature of 60 DEG C to 95 DEG C so as to produce ferric phosphate precipitates, and carrying out filtrating and washing, thereby obtaining lithium-containing filtrate and ferric phosphate. The method provided by the invention is simple in process, continuous in cycle, low in cost and easy to industrialize and is environmentally friendly; the recovery rate of Li, Fe and P reaches 95% or more, subsequent prepared FePO4 is low in impurity content, the particle size is 1 to 6 microns, is uniform and is narrow in distribution, and the morphology is controllable, so that the FePO4 is battery-grade ferric phosphate.