As a highly sensitive detection technology, incoherent broadband cavity enhanced absorption spectroscopy (IBBCEAS) have successfully measured a variety of trace gases. According to the principle of cavity enhanced absorption spectroscopy, if the accurate concentration of the target gas, the curve of the mirror reflectance, effective absorption path length, the light intensity of the absorbing gas and non-absorbing gas are known, the absorption cross section of the absorption gas can be measured. The accurate measurements of absorption cross section are necessary for satellite retrievals of atmospheric trace gases and the atmospheric research.　This paper describes an incoherent broadband cavity enhanced absorption spectroscopy(IBBCEAS) instrument with 365 nm LED as the light source for measuring absorption cross section of SO2 from 357 to 385 nm which is arising from the spin-forbidden a3B1—X1A1 transition. In comparison to the literature absorption cross section of SO2, and correlation coefficient r is 0.997　3. The result shows the potential of the IBBCEAS system for measuring weak absorption cross section.