Hirota's bilinear form for the Complex Modified Korteweg-de Vries-II equation (CMKdV-II) U-t - 6 vertical bar U vertical bar U-2(x) + U-xxx = 0 is derived. We obtain one- and two-soliton solutions analytically for the CMKdV-II. One-soliton solution of the CMKdV-II equation is obtained by using finite difference method by implementing an iterative method. Copyright (C) 2009. O. Akin and E. Ozugurlu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.