Concerning the problem that the performance analysis method of Luby Transform (LT) codes under Gaussian elimination decoding algorithm is complicated and inaccurate, a novel performance analysis method based on probability transfer function was proposed. Firstly, for two LT codes with simple uniform degree distribution, the precise performance was studied and its quantitative expression was given. Secondly, the general LT code was investigated, and a simple but effective qualitative analysis method was proposed. Finally, the simulation work was done to verify the new method. In the comparison experiments with the traditional method which only gives the upper and the lower bounds of the rank of generated matrix, the maximum error of performance analysis results for simple uniform degree LT codes reduces to 0.0124, and the complexity of general LT codes decrease to O( k ²). Theoretical analysis shows that the proposed method can effectively guide the optimization design of LT codes in communication area.