As a kind of channel coding, fountain code is an important technique to solve the interference of atmosphere on free space optical communication. Degree distribution is a key factor affecting the performance of fountain code. In the light of the degree distribution of fountain code, robust soliton distribution and fixed degree distribution is firstly analyzed from the principle and the deficiency on the performance, after that, the fixed degree distribution function is improved, then a new joint degree distribution design is proposed to combine the moved robust soliton distribution with the improved fixed degree distribution by a proportion ratio. The simulation results show that the decoding performance of the joint degree distribution proposed in this paper is much higher than the robust soliton distribution and fixedness distribution.