Recently, the application of response surface methodology (RSM) to robust parameter design has attracted a great deal of attention. In some cases, experiments are very expensive and may require a great deal of time to perform. Central composite designs (CCDs) and Box and Behnken designs (BBDs), which are commonly used for RSM, may lead to an unacceptably large number of experimental runs. In this paper, a supersaturated design for RSM is constructed and its application to robust parameter design is proposed. A response surface model is fitted using data from the designed experiment and a stepwise variable selection. An illustrative example is presented to show that the proposed method considerably reduces the number of experimental runs, as compared with CCDs and BBDs. Numerical experiments are also conducted in which type I and II error rates are evaluated. The results imply that the proposed method may be effective for finding the effects (i.e. main effects, two-factor interactions, and pure quadratic effects) of active factors under the ‘effect sparsity’ assumption. Copyright © 2010 John Wiley & Sons, Ltd.