The nonlinear spatial bending vibration equations of cantilevered fluid-conveying pipe with “large” symmetry breaking on the cross section were derived under the coordinate system of centroid principal axes of inertia. The Galerkin method was applied to discretize the vibration equations into a system of ordinary differential equations. The loss of stabilities of the fluid-conveying pipe in two principal transverse directions were investigated through numerical calculations based on the 6-mode Galerkin discretization equations of the original vibrations. The results show that, when the difference between the dimensionless bending stiffnesses in the two principal transverse directions is relatively significant, the pipe would not lose its stabilities in both principal directions simultaneously; when the difference of the two dimensionless bending stiffnesses does not exceed a certain value, the pipe may lose its stabilities in two principal directions simultaneously for specific mass ratio. For “simultaneous loss of instabilities” occurring in the non-hysteresis part of the two critical flow velocity curves, the pipe would flutter as the flow velocity increases, performing stable torus motion, stable periodic motion in the direction of greater stiffness, or stable periodic motion in the direction of smaller stiffness. If the “simultaneous loss of stabilities” occurs at the intersection of the hysteresis and non-hysteresis parts of the two critical flow velocity curves, the pipe would flutter no matter what happened to the flow velocity (increase or decrease), and then, if the pipe performs periodic motion in the direction of greater (smaller) stiffness when the flow velocity increases, the periodic motion would occur in the direction of smaller (greater) stiffnesses as the flow velocity decreases.