The re-parameterized inverse Gaussian distribution is a very useful distribution for statistics and it is applied to various fields, such as physics, engineering, biology, etc. It is also appropriate to analyze the right-skewed data. In this research, we were interested in studying the Fisher-information matrix and we wanted to find the covariance matrix to form asymptotic confidence ellipses of parameters for the re-parameterized inverse Gaussian distribution. We compared the coverage probability with the confidence coefficient of 0.98 of confidence ellipses with sample sizes of n= 10, 30, 50, 100, 1,000, and 10,000. The parameters of λ= 0.5, 1, 5, 10, 50 and θ= 0.5, 1, 5, 10, 50. The data were simulated by the composition method which they were repeated 10,000 rounds in each case with RStudio programming. The simulation results indicate that the value of coverage probability had been close to the confidence coefficient of 0.98 at the sample size of 10,000.