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In this paper we investigate the estimator for the rth power of the scale parameter in a class of exponential family under symmetric entropy loss L(θ, δ)= ν(θ/δ+δ/θ-2).An exact form of the minimum risk equivariant estimator under symmetric entropy loss is given, and the minimaxity of the minimum risk equivariant estimator is proved.The results with regard to admissibility and inadmissibility of a class of linear estimators of the form cT(X)+d are given, where T(X)～Gamma(ν,θ).