Inter-Satellite Optical Wireless Communication (Is-OWC) is regarded as the best choice for satellite communication because of its large throughput, low transmission power and high immunity to interference. To increase the availability of Is-OWC, it is required to implement a communication scheme that realizes lower latency and handles more traffic. In this paper, we propose a new Is-OWC system that uses multi-layer satellite constellation that applies uplink Non-Orthogonal Multiple Access (NOMA) to achieve delay suppression and increased throughput. In our proposed scheme, to distribute packets and reduce queue delay in each satellite, each communication path is adapted to the distance between the terrestrial transmitter and receiver. Simulation results validate the performance of our NOMA model is better than that of the conventional OMA model. Furthermore, the results showed that the BER of our model is improved by introducing the original algorithm to optimize the transmission power and the allocated sub-band of each satellite for the NOMA transmission. As a result, comparison of the latency between the proposed model using LEO and MEO satellites and the conventional model using only LEO satellites, the proposed model realizes delay suppression. The difference between the two models becomes more significant as the number of sessions in the entire network increases.