We experimentally demonstrate multiple dispersive waves (DWs) emitted by multiple mid-infrared solitons in a birefringence tellurite microstuctured optical fiber (BTMOF). To the best of our knowledge, this is the first demonstration of multiple DWs in the non-silica fibers. By using a pulse of ~80 MHz and ~200 fs emitted from an optical parametric oscillator (OPO) as the pump source, DWs and solitons are investigated on the fast and slow axes of the BTMOF at the pump wavelength of ~1800 nm. With the average pump power increasing from ~200 to 450 mW, the center wavelength of the 1st DW decreases from ~956 to 890 nm, the 2nd DW from ~1039 to 997 nm, the 3rd DW from ~1101 to 1080 nm, and the 4th DW from ~1160 to 1150 nm. Meanwhile, obvious multiple soliton self-frequency shifts (SSFSs) are observed in the mid-infrared region. Furthermore, DWs and solitons at the pump wavelength of ~1400 and 2000 nm are investigated at the average pump power of ~350 mW.