Quality of Service (QoS) requirement is denoted by the range to support the flexible and heterogeneous QoS. According to the microeconomics, a Kelly/PSPmodel-based pricing strategy is presented to support the inter-group fairness. The Equal Link Split Downstream (ELSD) method is adopted to support the intra-group fairness. Based on the parallelized Firing Coupled Neural Network (FCNN), the multi-constrained QoS multicast routing algorithm is designed. Simulation results have shown that the proposed mechanism is both effective and efficient, and its runtime efficiency is higher than the corresponding serialized one.