Common corn starch-lauric acid complex (CSLA) was prepared by extrusion treatment combined with cool storage. The effects of extrusion treatment combined with cool storage on the gelatinization degree, complexing index, thermal properties, crystal structure and digestive properties of CSLA were systematically investigated by means of differential scanning calorimetric analysis (DSC) and X-ray diffraction analysis (XRD). The results showed that compared with extrusion treatment, extrusion treatment combined with cool storage was beneficial to the formation of common corn starch-lauric acid complex, the complexing index increased from 29% to 35%, and the relative crystallinity increased from 25.20% to 31.82%. Extrusion treatment combined with cool storage can reduce the digestibility of the compound and increase the content of RS from 38.07% to 49.82%. The results of thermal properties showed that extrusion treatment combined with cool storage made common corn starch and lauric acid form VI- type complex with low thermal stability, and the melting temperature was 89.95~101.33 ℃, while common corn starch and endogenous lipids formed a VII- type complex with high thermal stability, and the melting temperature was 106.73~ 117.48 ℃. The results can provide reference for the preparation of starch-fatty acid complex with low digestibility and the preparation of anti-digestibility starch food.