We propose a bend-insensitive distributed Brillouin optical fiber sensing by using a singlemode-multimode-singlemode optical fiber structure for the first time to the best of our knowledge. The sensing fiber is a graded-index multimode fiber (GI-MMF) sandwiched by two standard single-mode fibers (SMFs) with central-alignment splicing at the interface between GI-MMF and SMF to excite the fundamental mode in GI-MMF. The sensing system can resist a minimal bend radius of 1.25mm while maintain the measurement performance, with which the measured coefficients of strain and temperature are 421.6MHz/% and 0.826MHz/°C, respectively. We also demonstrate that the higher-order modes excited in GI-MMF can be easily influenced by bending, so that exciting the fundamental mode is essential for bend-insensitive distributed sensing.