Enabling the inter-domain routing with end-to-end Quality of Service (QoS) guarantees, remains a challenge for the next generation Internet. Most of the existing research in QoS routing has been done considering a single domain. However, extending the QoS routing to the inter-domain level faces two major challenges: the scalability and the domain autonomy. In this paper, we propose a novel inter-domain QoS routing algorithm based on a hybrid computation scheme, named HID-MCP. The hybrid computation scheme combines the on-demand computation scheme and the pre-computation schemes taking benefits from these two computation schemes. Particularly, the hybrid computation allows speeding up the response time while providing a high success rate. Moreover, our algorithm reinforces the domain autonomy and solves the scaling problem by distributing the computations between domains. Extensive simulations confirm the efficiency of our algorithm in terms of the success rate and the computational complexity.