We present theoretical investigation of a single magnetic impurity in a d-wave superconductor using the large-N limit, It is shown that Kondo screening occurs only in the presence of particle-hole asymmetry. We find analytical expressions for the Kondo temperature, magnetic susceptibility, and scattering matrix near the phase transition. The results are generalized for the density of states vanishing with an arbitrary exponent. Also we briefly study the modifications of the theory for the case of a nonmagnetic impurity which induces a staggered spin configuration on nearby copper atoms.