We show how an extremal Reissner-Nordstrom black hole can be obtained by wrapping a dyonic D3-brane on a Calabi-Yau manifold. In the orbifold limit T-6/Z(3), We explicitly show the correspondence between the solution of the supergravity equations of motion and the D-brane boundary state description of such a black hole. (C) 1998 Elsevier Science B.V. All rights reserved.