Multicasting is an efficient and effective approach for supporting content distribution based on the current Internet infrastructure. In this paper, we have proposes the source-initiated CRMA (Cycle-breaking Rollback Multicast Routing Algorithm), which is a congestion-aware QoS (Quality of Service) based multicast routing algorithm. CRMA attempts to achieve the objective of minimizing network congestion conditions while satisfying bandwidth and end-to-end path delay requirements from users. Our proposed approach has several features: (1) It construct a shared symmetric distribution tree for multicast source(s) and its members rather than the conventional approach of constructing multicast tree. (2) CRMA combines the multicast path computation with resource allocation through introducing the WFQ (Weighted Fair Queuing) packet scheduling into path computation. (3) CRMA can be easily implemented and integrated into the common shortest path router architecture without a thorough adjustment. Through extensive simulations, we demonstrate that our CRMA can effectively reduce the cost, which is the reflection of network congestion conditions, of the computed multicast tree, compared to other proposed multicast routing schemes.