Abstract: Based on the fractal theory and the numerical simulationmethod, the curres of the height of imbibition and the mass ofimbibition against time are obtained for a power law liquid in a singletortuous capillary. The results show that the effect of the gravity may be neglectedat the initial stage of capillary rise and the effect of the gravity becomesimportant as time goes on. The maximum equilibrium height of imbibition fora power law liquid in a single tortuous capillary is found to be a functionof the capillary diameter \lambda and the density \rho of the power lawliquid, and independent of the tortuousity of a single tortuous capillaryand the power exponent n. Meanwhile, the rise velocity increases with the decreaseof the power exponent n at the initial stage of capillary rise. And the larger thetortuousity fractal dimension D_T , the more the mass of imbibition atequilibrium will be.