The invention belongs to the technical field of biogas treatment, and particularly relates to a biogas desulfurization and purification process. Hydrogen sulfide in biogas is absorbed through an absorption tower, the liquid-gas ratio of an absorption liquid to the sulfur-containing biogas is (0.01-0.02):1, and the absorption liquid comprises water, complexing iron, complexing ferrous iron, N,N-dihydroxyethylpiperazine, 7-diethylamino-4-methylcoumarin, 2-hydroxymethyl-15-crown ether-5, sodium carbonate and a sodium bicarbonate buffer system, wherein the concentration of the iron element in thecomplexing iron is 300-800 mg / L, the concentration of the iron element in the complexing ferrous iron is 500-700 mg / L, the concentration of the N,N-dihydroxyethylpiperazine is 30-45 mg / L, the concentration of the 7-diethylamino-4-methylcoumarin is 3-6 mg / L, the concentration of the 7-diethylamino-4-methylcoumarin is 15-20 mg / L, and the pH value of the solution is controlled to be 7.5-9.0 through asodium carbonate and sodium bicarbonate buffer system. Compared with the prior art, the biogas desulfurization and purification process provided by the invention has the advantages of simple desulfurization process, high desulfurization efficiency and stable desulfurizer performance, and can be stored for a long time without deterioration.