Numerical calculations of orbit evolutions of model and real bodies of the Kuiper belt are carried out on prolonged intervals. Gravitational perturbations from all major planets and in addition the Pointing — Robertson non-gravitational effect for small particles are taken into account. It is shown that a wide orbit scattering of the real Kuiper belt bodies in semimajor axis — eccentricity co-ordinates is explained by their evolution during millions of years. The conclusion is made that the relative contribution of large bodies and meteor particles from the Kuiper belt to the near-Earth complex should be very small.