Homogeneity of dispersion parameters is a standard assumption in inverse Gaussian regression analysis. However, this assumption is not necessarily appropriate. This paper is devoted to the test for varying dispersion in general inverse Gaussian linear regression models. Based on the modified profile likelihood (Cox & Reid, 1987), the adjusted score test for varying dispersion is developed and illustrated with Consumer- Product Sales data (Whitmore, 1986) and Gas vapour data (Weisberg, 1985). The effectiveness of orthogonality transformation and the properties of a score statistic and its adjustment are investigated through Monte Carlo simulations.