The bacterial flagellar motor is an ion-driven rotary machine in the cell envelope of bacteria. Using a gold nanoparticle as a probe, we observed the precession of flagella during rotation. Since the mechanism of flagella precession was unknown, we investigated it using a combination of full simulations, theory, and experiments. The results show that the mechanism can be well explained by fluid mechanics. The validity of our theory was confirmed by our full simulation, which was utilized to predict both the filament tilt angle and motor torque from experimental flagellar precession data. The knowledge obtained is important in understanding mechanical properties of the bacterial motor and hook.