Our model of meteor shower forecasting (described in Paper I) is applied to the Leonid shower. This model is based on the "dirty snowball" model of comets, and on heavy numerical simulation of the generation and evolution of meteoroid streams. The amount of dust emitted by comet 55P/Tempel-Tuttle is computed. A statistical weight is associated to each simulated particle. This weight represents the real amount of meteoroids released by the comet. Particles close to the Earth are examined. There is no unique set of initial conditions (velocity and angle of ejection) for them to reach the Earth at the time of the shower. The shape of the metoroid stream projected on the ecliptic is not elliptical, due to non-gravitational forces and ejection processes. The mixing of particles is revealed to be very efficient. A comparison between observations and predictions of Leonid meteor showers is done. The time of maximum is found to be very accurate, except for certain years (1999 in particular). This problem is common to all models. The level of the predicted shower is obtained through a fit of the size distribution index s = 2.4 ± 0.1. This model provides a unique opportunity to derive cometary parameters from meteor shower observations. Leonid meteor shower forecasts are provided for years up to 2100. The next storm is expected in 2034. © ESO 2005.