A novel nonlinear incremental optimization algorithm MH-iSAM2 is developed to handle ambiguity in simultaneous localization and mapping (SLAM) problems in a multi-hypothesis fashion. It can output multiple possible solutions for each variable according to the ambiguous inputs, which is expected to greatly enhance the robustness of autonomous systems as a whole. The algorithm consists of two data structures: an extension of the original Bayes tree that allows efficient multi-hypothesis inference, and a Hypo-tree that is designed to explicitly track and associate the hypotheses of each variable as well as all the inference processes for optimization. With our proposed hypothesis pruning strategy, MH-iSAM2 enables fast optimization and avoids the exponential growth of hypotheses. We evaluate MH-iSAM2 using both simulated datasets and real-world experiments, demonstrating its improvements on the robustness and accuracy of SLAM systems.