We study one-dimensional tight-binding models with a slowly varying, incommensurate off-diagonal modulation on the hopping amplitude. Interestingly, we find that the mobility edges can appear only when the off-diagonal (hopping) disorder is included, which is different from the known results induced by the diagonal disorder. We further study the situation where the off-diagonal and diagonal disorder terms (the incommensurate potential) are both included and find that the locations of mobility edges change significantly and the variation of the mobility edge becomes nonsmooth. To obtain these results, we first identify the exact expressions of mobility edges of both models by using asymptotic heuristic arguments, and then verify the conclusions by utilizing several numerical diagnostic techniques, including the inverse participation ratio, the density of states, and the Lyapunov exponent. These results will provide perspectives for future investigations on the mobility edge in low dimensional correlated disordered systems.