Primary assumption in most problems of elasticity theory in petroleum geophysics is that the elastic media is isotropic. Laboratory experiments confirmed that most rocks are anisotropic. If in one medium, properties vary with directions, it is named as anisotropic. Knowledge about anisotropy reduces risk and cost of hydrocarbon production. In the present study, anisotropy of a carbonate reservoir in southwest of Iran has been evaluated based on available walkaway vertical seismic profile (VSP) data. First break times have been picked and using horizontal and vertical slowness concept anisotropic module is computed. Direct arrival times and slowness from wide–aperture walkaway VSP data acquired in a layered anisotropic medium is processed to find a direct estimate of the phase slowness surface associated with the medium at the depth of the receivers. The slowness surface fits by an estimated transversely isotropic medium with a vertical symmetry axis (a “Vertical Transverse Isotropic (VTI)” medium). While the method requires that the medium between the receivers and the surface be horizontally stratified, no further measurement or knowledge of that medium is needed. The results show that this method provides the accuracy in the range of qualified accuracy with absolute errors of about 0.01 and 0.025 for Thomson's anisotropy parameters ε and δ, respectively.