To satisfy the Quality of service (QoS) requirements of multimedia applications, satellite routing schemes should provide better QoS guarantees. A multipath Inter-satellite link (ISL) routing (MPIR) scheme is proposed for low earth orbit satellite networks, which employs genetic algorithm to implement ISL QoS routing. Moreover, several essential ingredients, such as fitness function, mutation probability, are designed. Furthermore, simulated annealing is introduced to handle population diversity. Simulation results demonstrate that MPIR achieves better QoS guarantees than High performance satellite routing (HPSR) on delay jitter, call blocking probability with bandwidth and delay constraints. Besides, ALBR has lower onboard computational requirements than HPSR.