Abstract: Applying a memory concept to numerical weather prediction and introducing a memorial function, an appropriate difference-integral equation which is called a selfmemorization one has been formulated. Meanwhile the spherical harmonic representation of the equation is drieved too. Setting up and solving the equation establish a new approach of numerical weather prediction. Using T42L9 spectral model as a dynamic kernel, a global self-memorial T42 model (SMT42) was setup, with which several cases of 15-day integration experiments were carried out. Compared with T42, SMT42 is much better in 500 hPa forecast in daily up to 15 days, whose root mean square error (RMSE) is significantly reduced.