Current quality of service (QoS) routing schemes for low earth orbit (LEO) satellites IP networks either neglect the varying population density or fail to guarantee end-to-end delay. As a remedy, QoS routing protocol based on mobile agent (QoSRP-MA) is proposed. QoSRP-MA is a source-based routing protocol. Once connection requests arrive, QoS mobile agents are dispatched from ingress satellite to explore routes, which migrate using satellite routing tables. Upon arriving in egress satellite, QoS mobile agents migrate back towards ingress satellite to reserve bandwidth. To construct satellite routing tables, load balancing routing algorithm based on mobile agent (LBRA-MA) is presented. In LBRP-MA, at regular intervals mobile agents launched on all satellites migrate autonomously to evaluate path cost and update routing tables. Moreover, path cost between source and destination is evaluated considering satellite geographical position as well as inter-satellite link (ISL) cost. Furthermore, ISL congestion index is considered to update routing table. Through simulations on a Courier-like constellation, it shows that QoSRP-MA can achieve guaranteed end-to-end delay bound with higher throughput, lower connection failing ratio and signaling overhead compared to high performance satellite routing (HPSR) scheme.