The invention discloses a flue gas desulfurization and denitrification device and method of a coal fired boiler, and relates to desulfurization and denitrification treatment of tail gas of a three-waste mixed fired boiler in the coal-to-gas industry, such as synthesized ammonia and methyl alcohol. The device is arranged behind an electric precipitator of a three-waste mixed fired boiler, and mainly comprises a precooler, a desulfurizer, a circulation pump, a hydrogen peroxide storage tank, an absorption liquid supplementing pump, a dilute sulphuric acid storage tank and the like; sulfur dioxide and nitric oxide in the tail gas are removed by utilizing the circulation absorption of a hydrogen peroxide solution in the desulfurizer with flue gas, and the generated dilute sulphuric acid is stored and sold.