Lithium thulium fluoride LiTmF4 is an insulating Van Vleck paramagnet with a giant magnetostriction. Magnetization of the tetragonalLiTmF4 single crystals was measured for the first time in the temperature range of 2–300 K and inmagnetic fields up to 55 kOe, oriented both parallel and perpendicular to theC4 symmetry axis. In particular the angular dependence of the magnetization in the basalplane was studied. The anisotropy of magnetization in this plane grows rapidly in highfields. The temperature dependence of the magnetization in the orientation is nonmonotonic and reproduced very well by the calculation in the framework of thecrystal field theory. The discrepancies between experimental and theoretical dependences inthe orientation in high magnetic fields are attributed to the magnetostriction effects.