Recently Bi2Te3 material has been discovered as a new type of quantum matter, a 3D topological insulator [1]. We report the observation of Shubnikov de Haas (SdH) oscillations on longitudinal (HllI) and transverse (Hl_I) magnetic field arising from surface state in single crystal Bi2Te3 layers. Single crystals of Bi2Te3 layers were prepared using the mechanical exfoliate method by cleaving thin layer from bulk crystalline Bi2Te3 samples [2]. From experimental data on SdH oscillations at temperature of 2.1-4.2 K, cyclotron effective mass, Dingle temperature and the quantum mobility of charge carriers are calculated. It was revealed, that the value of phase shift has made 0,5 both in parallel, and in perpendicular magnetic fields. The experimental value of phase shift of Landau levels index was defined by value n for limiting value of magnetic field H-1 = 0, as a result of linear extrapolation of dependence of experimental values of an index n from reciprocal magnetic field H-1. It is known, that phase shift is connected with Berry’s phase which is the integrated characteristic of orbit cyclotron curvature and the electron dispersion and is characteristic surface state. The results received in presented work confirm with the presence of surface state in Bi2Te3 layer and are compared to results on f Bi2Te3 films, wires and bulk samples [3,4].