Starting from the three-dimensional atmospheric dynamic equationsand based upon the phase path method, the linear transformation method is used here for transferring the nonlinear three-dimensional problem into a nonlinear two-dimensional problem. The nonlinear termsare expanded to the third order by a Taylor’s series in the neighbour-hood of the equilibrium point of the equations. Thus the nonlinear two-dimensional equations are all solved and explicit analytic solutionsto the three-dimensional nonlinear inertia-gravity waves are obtained.Analysis shows that with the nonlinear terms to the second order,the solutions are composed of the superposition of a cosine wave anda cnoidal wave, and with the nonlinear terms to the third order, the three-dimensional nonlinear inertia-gravity waves are satisfied by themodified Kortweg-de Vries equation and under given conditions, the solutions are composed of the superposition of two solitary waves. Inaddition, one exact implicit solution is found. The dynamic propertiesof all the solutions as mentioned above are discussed.