The frictional behavior of granular materials plays important roles in the movement of geo-materials in landslides and earthquake faults, and of industrial materials; many studies have been put forward to better understand the frictional behavior of granular materials under differing conditions. In this paper we report on laboratory experiments designed to explore the fundamental role of particle size and shear speed in the frictional instabilities for locally sheared granular materials subjected to large shear displacement. We used spherical glass beads with differing particle sizes (similar to 0.1 to 5.0 mm), and sheared them at differing speeds (gradually stepped from 0.005 to 50.0 mm/s in some cases) under a given normal stress of 200 kPa by employing a ring shear apparatus. Results showed that frictional instability occurred in some tests on glass beads with larger particle sizes, and such kind of frictional instability also appeared repeatedly with the progress of shearing. The frictional instabilities (stress drops) were constrained not only by the shear speed but also by the particle size. The magnitude and recurrence time of stress drop decreased with increasing shear speed for a given particle size, however, they increased with increase of particle size at the same shear speed. We evaluated the relationship between stress drop and recurrence time, and found that particle size had greater influence on frictional instability. We suggested that the formation and failure of force chains among the glass beads during larger shear displacement are the main reasons for this kind of frictional instability. (C) 2016 Elsevier B.V. All rights reserved.