In this paper, to find an approximate solution of general linear Fredholm integro-differential-difference equations (FIDDEs) under the initial-boundary conditions in terms of the Bessel polynomials, a practical matrix method is presented. The idea behind the method is that it converts FIDDEs to a matrix equation which corresponds to a system of linear algebraic equations and is based on the matrix forms of the Bessel polynomials and their derivatives by means of collocation points. The solutions are obtained as the truncated Bessel series in terms of the Bessel polynomials Jn (x) of the first kind defined in the interval [0,∞). The error analysis and the numerical examples are included to demonstrate the validity and applicability of the technique. © 2011 Taylor &Francis.