Inter-domain quality of service (QoS) routing is a challenging problem for today's Internet. This problem requires the computation of paths that cross multiple domains and meet different QoS constraints. In addition, the used computation methods must meet the constraints of confidentiality and autonomy imposed by the domains of different operators. Path computation element (PCE)-based architecture offers a promising solution for inter-domain QoS routing. It ensures the computation of end-to-end QoS paths while preserving the confidentiality and the autonomy of the domains. In this paper, we propose a novel hybrid end-to-end QoS path computation algorithm, named HID-MCP, for PCE-based networks. HID-MCP is a hybrid algorithm that combines the advantages of pre-computation and on-demand computation to obtain end-to-end QoS paths. Moreover, it integrates a crankback mechanism for improving path computation results in a single domain or in multiple domains based on the PCE architecture. Detailed analyses are provided to assess the performance of our algorithm in terms of success rate and computational complexity. The simulation results show that our algorithm has an acceptance rate of the requests very close to the optimal solution; precisely, the difference is lower than 1 % in a realistic network. Moreover, HID-MCP has a low computational complexity. Besides, our solution relies on the PCE architecture to overcome the limitations related to inter-domain routing such as domain autonomy and confidentiality.