Abstract: This paper studies the numerical caculat ion process of global weather forecast model which is based on spectral method.The model use the Eulerian U- V model. The atmosphere is divided into NLEN layers and these layers are defined by the pressures at the interfaces between the / half- levels0. The prognostic variables are presented by their values at / full- level0 pressures. Spectral method to discretize is used in horizontal direction and a semi- implicit
correction is used to dicretize in time.

Key words: spectral method;Eulerian reformation, semi- implicit correction