The 3D capillarity-driven grain growth process was simulated using a modified Potts Monte Carlo technique, starting from two initial microstructures with the grain size distributions well described by Weibull functions of b=2.96 and b=3.47, respectively. The process obeys the grain growth parabolic law very well, with the time exponent n very close to 0.5. The results show that the quasi-stationary grain size distributions finally turn to the same Weibull distribution with b=2.80±0.03 for two different initial microstructures and the grain face number distributions turn to a lognormal distribution. The two analytical 3D grain size distribution functions coincide with the two kinds of functions derived by Liu Guoquan and his coworkers recently based on the different grain growth rate equations.