Abstract: The growth behavior of voids located at the grain boundary is numerically simulated using the three dimensional finite element method considering crystal plasticity theory. To do that, a user material subroutine is created to describe the rate dependent crystal plasticity behavior. A two-grain model including a spherical void is developed, where the orientation of grain1 is (0, 45, 90), and the orientations of grain 2 are (35, 45, 90), (60, 45, 90) and (0, 0, 0) respectively, corresponding to cell A, B and C; the angle between grain boundary and X axis, , is 0, 45 and 60 respectively. Results show that the fracture mode depends on the orientation difference between the two grains. For cell B, with the largest orientation difference, the equivalent plastic strain along the grain boundary is also the largest, as well as the maximum equivalent plastic strain, meaning the unit cell is prone to fail in intergranular fracture. For cell C, with the smallest orientation difference, the equivalent plastic strain along grain boundary is low, and the unit cell is prone to fail in transgranular fracture. The maximum equivalent plastic strain along the grain boundary corresponds to the case of  = 45, where the unit cell is prone to fail in intergranular fracture.