Most of the existing reliability-based design optimization (RBDO) are not capable of analyzing data from multi-fidelity sources to improve the confidence of optimal solution while maintaining computational efficiency. In this paper, we propose a novel reliability-based multi-fidelity optimization (RBMO) framework that adaptively integrates both low- and high-fidelity data for achieving reliable optimal designs. The Gaussian process (GP) modeling technique is first utilized to build a hybrid surrogate model by fusing data sources with different fidelity levels. To reduce the number of low- and high-fidelity data, an adaptive hybrid learning (AHL) algorithm is then developed to efficiently update the hybrid model. The updated hybrid surrogate model is used for reliability and sensitivity analysis in solving a RBDO problem, which provides a pseudo optimal solution in the RBMO framework. An optimal solution that meets the reliability targets can be achieved by sequentially performing the adaptive hybrid learning at the iterative pseudo optimal designs and solving RBDO problems. The effectiveness of the proposed framework is demonstrated through three case studies.