Srivastava (1974, 1980) and Chaubey and Dwivedi (1982) investigated some estimators of mean of a normal population utilizing an estimate of the coeffcient of variation. However, the normal model may not hold for positive or positively skewed data, hence an alternative model may have to be employed. This paper uses the inverse Gaussian model for such data and extends the results of Chaubey and Dwivedi (1982) for the normal population to similar analysis for the inverse Gaussian population. It is found that the new estimator may result in large gains in effciency over the sample mean for large values of the coeffcient of variation.