The estimation of the function exp(aξ + bσ2) of normal parameters ξ and σ2on the basis of a random sampleX1, …,Xnis considered. This class of functions includes the mean, the median, and all moments of lognormal distribution. I show that the minimum variance unbiased estimator suggested by Finney (1941) can be substantially improved in terms of mean squared error. A similar result is established for the maximum likelihood estimator. I suggest for practice use the following generalized Bayes estimator when m = [(n+1)/2]: δ(X,Y) = exp(aX + (γ - β)Y) ∑k=0m(2m - k)!/k!(m - k)!(2βY)k/∑k=0m(2m - k)!/k!(m - k)!(2γY)k. Here X = ∑InXj/n, Y2= ∑1n(X1- X)2, and constants β and γ are determined by formulas β2= γ2− 2b + 2a/n, γ = 1.5(b-3a2/(2n)). This estimator is shown to be locally optimal for both small and large values of σ2. The results of numerical study of the quadratic risk show the superiority of this estimator over the mentioned traditional procedures.