Abstract. We determine the dimension of the Heliosphere (modulation region), radial diffusion coefficient and other parameters of convection-diffusion and drift mechanisms of cosmic ray (CR) long-term variation, depending on particle energy, the level of solar activity (SA) and general solar magnetic field. This important information we obtain on the basis of CR and SA data in the past, taking into account the theory of convection-diffusion and drift global modulation of galactic CR in the Heliosphere. By using these results and the predictions which are regularly published elsewhere of expected SA variation in the near future and prediction of next future SA cycle, we may make a prediction of the expected in the near future long-term cosmic ray intensity variation. We show that by this method we may make a prediction of the expected in the near future (up to 10-12 years, and may be more, in dependence for what period can be made definite prediction of SA) galactic cosmic ray intensity variation in the interplanetary space on different distances from the Sun, in the Earth's magnetosphere, and in the atmosphere at different altitudes and latitudes.