In this study, we suggest a collocation method to solve a class of the nonlinear differential equations under the mixed conditions in terms of the Bessel polynomials. The method is based on the matrix forms of the Bessel polynomials and their derivatives by means of collocation points. To illustrate the usefulness of this technique we apply it to some test problems and the comparisons are made with existing results. The results show the efficiently and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in Maple. © de Gruyter 2012.