The Ergodic Capacity-based Scheduling Algorithm(ECSA) is proposed to solve the problem of user access to the Satellite-Unmanned Aerial Vehicle(UAV) -Terrestrial Network(SUTN). Satellites transmit data to UAV via Free Space Optical(FSO). The UAV transmits data to the user via a wireless communication Radio Frequency(RF) link. ECSA algorithm firstly derives the Signal-to-Noise Ratios(SNRs) of UAV terminal and the client, then derives the Probability Density Function(PDF) of SNRs, and then calculate the user's Ergodic Capacity(EC) on the basis of probability density function. In the end, it calculate the objective function of the user based on the principles of fairness, combining with the EC of the user.The user with the greatest objective function value will access the channel. Simulation results show that compared with the rotational scheduling algorithm, the proposed ECSA algorithm can effectively improve the system capacity.