Gaussian space is a three-dimensional Gaussian hypersurfaceembedded in a four-dimensional Euclidean space. The curvature ofspace depends on the distance to the origin. At a large distance,such a space is practically Euclidean, and because of this thereare solutions to the Schroedinger equation that behave atinfinity like plane waves. Without introducing any additionalpotential, the problem of particle's scattering in the Gaussianspace is considered in semi-classical approximation. The role ofthe scattering center is played by the space itself, which isstrongly curved at the origin. In this paper the complete WKB(Wentzel-–Kramers–-Brillouin) solutions to the Schroedingerequation have been built. Approximate expressions for thescattering phase shifts were obtained. The total cross sectionenergy dependence was calculated numerically using these phaseshifts. Both results display the tendency of the cross section toa constant value at high energy regime.