The Levenberg-Marquardt Method (LMM) is applied in the present study to determine the optimal fin widths and heights of an impingement cooling heat sink module using a general purpose commercial code (CFD-ACE+). In this optimal heat sink design problem, the non-uniform fin widths and heights are chosen as the design variables. The objective of the present study is to minimize the system thermal resistance (R-th) of the fin array and to obtain the optimal dimensions of heat sink. The results obtained by numerical experiments demonstrate that by utilizing the optimal heat sink and operating at the design condition Re = 15,000, R-th can be decreased by 3.10% and 1.20% when compared with the original and Yang and Peng's (2008) [1] heat sinks, respectively. Nu and COE can be increased by 3.20% and 3.20%, respectively, when compared with the original heat sink, and these parameters can be increased by 1.22% and 1.18%, respectively, when compared with the optimal heat sink proposed by Yang and Peng (2008) [1]. Consequently, the thermal performances of optimal impingement heat sink can be improved. (C) 2014 Elsevier Ltd. All rights reserved.