In this paper, first we use the already defined gamma-divergence and then introduce a goodness of fit test for exponentiality. This divergence measure is very robust with respect to outliers. In order to construct test statistics, two estimators are used as estimators of gamma-divergence. In the first one we consider the gamma-divergence of the equilibrium distribution function, which is well defined on the empirical distribution function (EDF) and is proposed as an EDF-based goodness of fit test statistic. The second one is an estimator in manner of Vasicek entropy estimator. Critical values of test statistics are computed by Monte Carlo simulations. Then, the power values of the proposed tests are compared with some known competing tests under various alternatives. Simulation results indicate that in comparision with the other tests statistics, our mentioned test statistics almost in most of the cases have higher power. Finally, two examples containing outliers illustrate the importance and use of the proposed tests.

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