This paper deals with the statistical inference for the geometric process (GP), in which the time until the occurrence of the first event is assumed to follow inverse Rayleigh distribution. The maximum likelihood (ML) method is used to derive the estimators of the parameters in GP. Asymptotic distributions of the ML estimators are obtained which help us to construct confidence intervals for the parameters and show the consistency of these estimators. The performances of the ML estimators are also compared with the corresponding non-parametric modified moment estimators in terms of bias, mean squared error and Pitman nearness probability through an extensive simulation study. Finally, a real data set is provided to illustrate the results.