The LED caustic beam is generated by LED light source. A method of using cross-spectral density function and superposition of multi-spectral is proposed to calculate the intensity distribution of the LED caustic beam through the axicon. The influence of parameters such as dispersion on caustic beam is theoretically and experimentally demonstrated. The influence of the transmission distance on the LED caustic beam is further studied. It is found that the outer contour of the caustic beam becomes larger and the central light spots symmetrically split into light spot array as the transmission distance increases. Meanwhile, the central intensity decreases correspondingly, and the contrast of the light spot array decreases gradually. It will evolve into an approximately hollow beam eventually. This research results enrich the connotation of caustic beam, and provide a theoretical basis and experimental evidence for the practical application of LED caustic beam.