Using peanut shells, a sustainable agricultural waste product, as its raw material, the acid group-modified biochar (AMBC) was prepared through phosphoric acid activation, partial carbonization, and concentrated sulfuric acid sulfonation for efficient removal of lead ion from aqueous solutions. Characterization techniques such as N2 isothermal adsorption–desorption, SEM, XRD, FT-IR, TG-DTA, and acid–base titration were utilized to fully understand the properties of the AMBC. It was found that there were high densities of acidic oxygen-containing functional groups (-SO3H, -COOH, Ph-OH) on the surface of the AMBC. The optimal adsorption performance of the AMBC for Pb(II) in water occurred when the initial concentration of Pb(II) was 100 mg/L, the pH was 5, the dosage of the adsorbent was 0.5 g/L, and the contact time was 120 min. Under the optimal conditions, the removal ratio of Pb(II) was 76.0%, with an adsorption capacity of 148.6 mg/g. This performance far surpassed that of its activated carbon precursor, which achieved a removal ratio of 39.7% and an adsorption capacity of 83.1 mg/g. The superior adsorption performance of AMBC can be caused by the high content of acidic oxygen-containing functional groups on its surface. These functional groups facilitate the strong binding between AMBC and Pb(II), enabling effective removal from water solutions.