We study a single impurity effect on the local density of states in a d-wave superconductor accounting for the momentum-dependent impurity potential. We show that the anisotropy of the scattering potential can alter significantly the spatial dependence of the quasiparticle density of states in the vicinity of the impurity.A search for the symmetry of the cuprate superconducting state involves among others theoretical studies of the disordered systems [1,2,3]. The most direct probe of a simple defect impact on superconductivity is provided by the scanning tunneling microscopy (STM) measurement of the position-dependent quasiparticle density of states. The STM images of Zn and Ni substitutions at the planar Cu sites in Bi 2 Sr 2 CaCu 2 O 8+δ reveal a distinct four-fold symmetry of the local density of states (LDOS) [4,5] predicted for the d-wave superconductor response to disorder [6,7]. In addition to providing detailed information on the superconducting state, this kind of experiment may shed light on the nature of the quasiparticle scattering centers. Although the main feature of the four-fold symmetry of the tunneling currents is captured by the model of isotropic impurity scattering the observed spatial dependence of the quasiparticle density of states is far more complex, and may originate from a non trivial structure of the impurity potential. This aspect of the quasiparticle scattering process has been raised in the discussion of macroscopic measurements in these compounds [8,9,10,11]. It has been shown that the unexpected for the d-wave superconductivity weak impurity-induced suppression of the critical temperature can be understood within a scenario of a momentum-dependent (anisotropic) impurity scattering potential [12,13,14,15]. In the present paper we discuss the effect of anisotropic impurity potential on the local density of states in the vicinity of a single impurity and verify to what extend this scenario can reproduce the STM maps of Bi 2 Sr 2 CaCu 2 O 8+δ . There are studies of the momentum-dependent impurity scattering which indicate the existence of the impurity-bound states even for the potential strength far from resonant [17]. Therefore, we focus here on the symmetry of the LDOS and its spatial dependence. For this purpose and for analytical simplicity we consider scattering in the Born approximation. Hereafter we show that the anisotropy of the scattering potential alters the local density of states in the d-wave superconductor but preserves its tetragonal symmetry. Compared to the effect of the isotropic impurity potential it enhances the spatial variation of the quasiparticle density of states and can lead to a longrange spatial modulation of the LDOS spectra. We note that the anisotropy of the impurity potential, if the same as the anisotropy of the superconducting order parameter, enhances the relative magnitude of oscillations in the LDOS for the direction of a gap maximum, especially in the vicinity of the impurity, whereas the impurity potential with maxima in the nodal region inver...