This article considers risk-averse simulation optimization problems, where the risk measure is the well-known Average Value-at-Risk (also known as Conditional Value-at-Risk). Furthermore, this article combines Taguchi's robustness with Response Surface Methodology (RSM), which results in a novel, robust RSM to solve such risk-averse problems. In case the risk-averse problem is convex, the conic quadratic reformulation of the problem is provided, which can be solved very efficiently. The proposed robust RSM is applied to both an inventory optimization problem with a service-level constraint and a call-center problem; the results obtained for the risk-averse problem and its benchmark problem, where the risk measure is the variance, are intuitively sound and interesting. (C) 2010 Elsevier By. All rights reserved.