In wireless transmission, the sudden declination of channel quality would result in the rise of error percentage, when a certain number of coded symbols have been received the input symbols are used to be decoded, which would slow down the decoding speed. Hence, to improve the success probability and speed of partial decoding of short code length LT codes, in this paper, we propose the Fast Belief Propagation (FBP) decoding algorithm, which uses the swap heuristic method and the transformation of the triangular matrix not only to enhance the decoding success proportions but also to reduce the decoding delay. According to analysis and experiment, FBP decoding algorithm is better than the conventional methods, Belief Propagation (BP) and Gaussian Elimination (GE). In the simulation, while the length of the source symbols is 128 bits, the probability of the FBP decoding is 48.09 percent higher than traditional ones at the most and its decoding complexity and time consumption are less than GE.