The invention provides an LEO uplink asynchronous collaborative multiple access method applied to a GEO/LEO network. At a GEO receiving node, the collision problem generated by LEO uplink messages during asynchronous random access is solved through a successive interference cancellation method. The method comprises the steps that various LEO nodes code and modulate message packets and then send the message packets out, and the message packet sent by each LEO node is at least received by two GEO nodes; various GEO nodes return the received message packets to a gateway station on the ground; anda demodulation device of the gateway station is provided with a slide detection window for each GEO node correspondingly for message detection, coding and demodulation. During demodulation, cross-node collaborative interference cancellation is conducted by means of heterogeneous delay and the uncollided message packets to restore the collided message packets. According to the method, system synchronization is not needed, the power and signaling overhead introduced by system synchronization is reduced, and the power consumption of the terminal is reduced.