Experimental studies on the folding and unfolding of large multi-domain proteins are challenging, given the proteins' complex energy landscapes with multiple intermediates. Here, we report a mechanical unfolding study of a 346-residue, two-domain leucine binding protein (LBP) from the bacterial periplasm. Forced unfolding of LBP is a prerequisite for its translocation across the cytoplasmic membrane into the bacterial periplasm. During the mechanical stretching of LBP, we observe that 38% of the unfolding flux followed a two-state pathway, giving rise to a single unfolding force peak at ~70 pN with an unfolding contour length of 120 nm in constant-velocity single-molecule pulling experiments. The remaining 62% of the unfolding flux followed multiple three-state pathways, with intermediates having unfolding contour lengths in the range ~20-85 nm. These results suggest that the energy landscape of LBP is complex, with multiple intermediate states, and a large fraction of molecules go through intermediate states during the unfolding process. Furthermore, the presence of the ligand leucine increased the unfolding flux through the two-state pathway from 38% to 65%, indicating the influence of ligand binding on the energy landscape. This study suggests that unfolding through parallel pathways might be a general mechanism for the large two-domain proteins that are translocated to the bacterial periplasmic space.