This paper presents the application of an improved smoothed particle hydrodynamics (SPH) method to simulate violent liquid sloshing in a rotating liquid tank. Two major modifications are incorporated into the SPH method. Firstly, the kernel gradient correction (KGC) is used to improve the computational accuracy with precise and smooth pressure field. Secondly, a coupled dynamic solid boundary treatment (SBT) is used to remove the numerical oscillation near the solid boundary and to prevent unphysical particle penetration. The dynamic response of the sloshing system and the change of the pressure profiles are investigated in detail while the SPH simulations are conducted under different external excitations and different water waves. The results shows that improved SPH method can describe violent deformation and break-up of free surfaces accurately, and obtain accurate pressure field.  It is revealed that for small amplitude liquid sloshing, the linear wave theory can apply and free surface does not break up.  For liquid sloshing with strong nonlinear effects, free surface evolves violently with breakup and impinging onto bulky water and solid walls, and therefore the linear wave theory is no longer valid.  A circular frequency deviated from the natural frequency from linear wave theory may produce bigger maximal pressure load than the case with equivalent natural frequency.