The Background Field Method is a quantization procedure which preserves the gauge invariance of a theory in each intermediate step. It was introduced by DeWitt and others for 1-loop calculations. It was then extended for 2-loops by 'tHooft and improved by DeWitt, Boulware and Abbott [1]. In this work the method is applied to quantize the SUSY Yang-Mills-Chern-Simons N=1 model in the absence of matter in (2+1) space-time dimensions. This model was already studied by Ruiz-Ruiz and van Nieuwenhuizen [2] using component fields. Here we use superfields formalism. The divergent supergraphs are classified up to 2-loops using an extended version of A. F. Ferrari's Mathematica package SusyMath [3]. In a next step, matter fields are going to be included as well. [1] L. F. Abbott, Acta. Phys. Pol. B13 (1982) 33-50. [2] F. Ruiz-Ruiz and, P. van Nieuwenhuizen, Lectures on Supersymmetry and Supergravity in 2+1 Dimensions and Regularization of Supersymmetric Field Theories, Mexican School on Gravitation and Mathematical Physics, Tlaxcala, Mexico, 1 (1996) 7, physics-2. [3] Ferrari, A. F., SusyMath: A Mathematica package for quantum superfield calculations, Comput. Phys. Commun. 176 (2007) 334.