A new kind of Lagrange function by variational principle of liquid sloshing in pitching tank is build. Based on this, the analytical solution of liquid nonlinear sloshing in pitching tank can be investigated. In the paper, the Taylor series about wave elevation function in the liquid free surface of velocity potential function is derived. After this, the nonlinear equations of free surface kinetic boundary condition and dynamic boundary condition is gained. Then, by supposing the solution in the form of the superposition of each dominated harmonic wave, the corresponding algebraic equations about unknown coefficients by Harmonic Balance Method (HBM) is derived. Last, the algebraic equations are solved by Broyden method. By the example of a two-dimensional, rigid, rectangular, open tank without baffles, the liquid large amplitude sloshing problem is investigated. As for the amplitude of liquid sloshing, comparison between theory and experiment show good agreement at certain frequency range. And at the same time, the phenomenon of zero shift at the liquid surface is found evidently.