As an indispensable solution for wide coverage and ubiquitous connectivity， satellite communication plays an important role in practical applications， including civilaviation air traffic management and emergency communication. To improve the spectral efficiency and transmission rate of satellite communication system， we propose an efficient uplink/downlink non-orthogonal multiple access （NOMA） transmission scheme combining spot beam with NOMA technology. Then， based on the assumption that the satellite links experience shadowed-Rician（SR） fading while the perfect and imperfect successive interference cancellation （SIC） are seperately adopted at receivers. We derive the closed-form expression for the ergodic capacity of the proposed scheme. Finally， simulation results are given to validate the theoretical analysis and the performance improvement compared to the orthogonal multiple access （OMA） scheme. The effects of various parameters are further revealed on the system performance， such as channel fading coefficient， power allocation fraction and residual interference level.