Bubble motion in non-Newtonian fluids is widely present in various industrial processes such as crude oil extraction, enhancement of boiling heat transfer, CO₂ sequestration and wastewater treatment. System containing non-Newtonian liquid, as opposed to Newtonian liquid, has shear-dependent viscosity, which can change the hydrodynamic characteristics of the bubbles, such as their size, deformation, instability, terminal velocity, and shear rate, and ultimately affect the bubble rising behaviors. In this work, the dynamic behavior of bubble rising in a shear-thickened fluid is studied by using an incompressible lattice Boltzmann non-Newtonian gas-liquid two-phase flow model. The effects of the rheological exponent n, the Eötvös number (Eo), and the Galilei number (Ga) on the bubble deformation, terminal velocity, and the shear rate are investigated. The numerical results show that the degree of bubble deformation increases as Eo grows, and the effect of n on bubble deformation degree relates to Ga. On the other hand, the terminal velocity of the bubbles increases monotonically and nonlinearly with Ga for given Eo and n, and the effect of n on the terminal velocity of the bubbles turns stronger as Ga increases. When Ga is fixed and small, the terminal velocity of the bubble increases and then decreases with the increase of n at small Eo, and increases with the increase of n when Eo is large; but when Ga is fixed and large, the terminal velocity of the bubbles increases with the increase of n in a more uniform manner. In addition, regions with high shear rates can be found near the left end and right end of the bubble. The size of these regions grows with Eo and Ga, exhibiting an initial increase followed by a decrease as n increases. Finally, the orthogonal experimental method is used to obtain the influences of the aforementioned three factors on the shear rate and terminal velocity. The order of influence on shear rate is n, Ga and Eo which are arranged in descending order. For the terminal velocity, Ga has the greatest influence, followed by n, and Eo has the least influence.