Abstract This overview describes a brief history of the numerical weather prediction proposed by L.F. Richardson in 1922. He had a dream of forecasting weather based on time integration of basic equations of fluid mechanics that express the atmospheric circulation. However, his idea was not successful at that time, because he had neither enough meteorological data for initial condition nor a high-speed computer for numerical calculation. It was after World War II that his dream has come true owing to incredible development of electronic computers and increase of upper-air sounding data. Today, most meteorological offices in the world predict weather based on numerical simulations of the global atmospheric circulation. The numerical model used in Japan consists of three models: a meso-scale model which covers the region of East Asia with horizontal resolution of 10 km is nested in a regional model with 20 km resolution which is nested in a global model with 50 km resolution. The short-term forecast is based on a single calculation with the best initial condition, but 1 month forecast is based on statistics of 26 different simulations with slightly different initial conditions (ensemble forecast).