While the ant colony optimisation (ACO) can find the optimal path through a network, there are too many iterations and the convergence speed is also very slow. This paper proposes the Q-ACO QoSR based on convergence expectation to meet the requirement of OoS routing for a real-time and highly efficient network. This algorithm defines index expectation function of link, and proposes convergence expectation and convergence grads. As for the multi-constraint QoS routing model, the algorithm controls the iteration and searches the optimal path that meets the QoS restriction condition under the condition of the faster convergence. This algorithm can find the optimal path by comparing the convergence grads in a faster and larger probability. This algorithm improves the ability of routing and convergence speed.