In this paper an attempt is taken to compare the efficiency of linear method relative to the Maximum Likelihood (ML) method with the help of computer simulated data in estimating the parameters of two-parameter exponential distribution, a member of location-scale family of distributions. Nine parameter combinations are investigated each with five different sample size. Generalized variance (GV) due to Wilks (1932) is used to compare the relative efficiency. It is observed that linear method is on an average equally efficient as that of ML method in terms of GV. The performance of ML method is comparatively better for large samples.