It is of significance to comprehend the effects of rock microstructure on the tensile strength under different loading rates caused by mining disturbance. So, in this paper, three kinds of sandstones drilled from surrounding rocks in Xiao Jihan Coal to simulate the in situ stress state, whose average grain size is 30 mu m (fine grain, FG), 105 mu m (medium grain, MG), and 231 mu m (Coarse grain, CG), are selected with the calculation of optical microscopic technique and moreover processed to Brazilian disc (BD) to study the mechanical response of samples. The dynamic Brazilian tests of samples with three kinds of grain sizes are conducted with the Split Hopkinson Pressure Bar (SHPB) driven by pendulum hammer, which can produce four different velocities (V = 2.0 m/s, 2.5 m/s, 3.3 m/s, and 4.2 m/s) when the incident bar is impacted by pendulum hammer. The incident wave produced by pendulum hammer is a slowly rising stress wave, which allows gradual stress accumulation in the specimen and maintains the load at both ends of the specimen in an equilibrium state. The results show that the dynamic strength of three kinds of BD samples represented loading rates dependence, and FG sandstones are more sensitive for loading rates than MG and CG samples. Moreover, the peak strength is observed to increase linearly with an increasing stress rates, and the relationship between the dynamic BD strength and stress rates can be built through a linear equation. Finally, the failure modes of different grain sizes are discussed and explained by microfailure mechanism.