Inference for the mean of a normal distribution with known coefficient of variation is of special theoretical interest be- cause the model belongs to the curved exponential family with a scalar parameter of interest and a two-dimensional minimal sufficient statistic. Therefore, standard inferential methods cannot be directly applied to this problem. It is also of practical interest because this problem arises naturally in many environmental and agriculture studies. In this paper we proposed a modified signed log likelihood ratio method to obtain inference for the normal mean with known coeffi- cient of variation. Simulation studies show the remarkable accuracy of the proposed method even for sample size as small as 2. Moreover, a new point estimator for the mean can be derived from the proposed method. Simulation studies show that new point estimator is more efficient than most of the existing estimators.