Generally, reactive powder concrete (RPC) contains steel fibers often exposed to aggressive environments. Steel fibers in such RPCs are subjected to corrosion in-service, which can significantly change the mechanical properties of the structural components. In this paper, basalt fibers were used to replace steel fibers for preparing a new basalt fiber modified reactive powder concrete (BFRPC). The bending resistance of BFRPC beams was studied, and the crack propagation and failure type of BFRPC beam were monitored by acoustic emission (AE). During the bending test, the failure type of BFRPC was evaluated by AE. Besides, the effects of notch and interfacial damage on the bending resistance and failure type were also studied. During the test, ordinary Reactive Powder Concrete (RPC) without basalt fibers was used as a reference. Results revealed that failure type of the RPC beam and BFRPC beam was mainly caused by shear failure. The notch increased the number of tensile cracks in the beam failure crack, resulting in a decrease in the bending resistance of RPC beam and BFRPC beam. Besides, basalt fiber could improve the toughness and bending resistance of BFRPC beam and increase resistance of the BFRPC beam to notch and interface damage.