One-parameter exponential regression is one of the most common and widely used models in several fields, to estimate the parameters of the one-parameter exponential regression model use the ordinary least square method but this method is not effective in the presence of outlier values, so robust methods were used to treat outlier values in the one-parameter exponential regression model are to estimate the parameters using robust method (Median-of-Means, Forward search, M-Estimation), and the simulation was used to compare between the estimation methods with different sample sizes and assuming four ratios from the outliers of the data (10%, 20%, 30%, 40%). And the mean square error (MSE) was made to reach the best estimation method for the parameters, where the results obtained using the simulation showed that the forward search is the best because it gives the lowest mean of error. On the practical side, expenditure and revenue data were used to estimate the parameters of the one-parameter exponential regression, where the data was tested, it appeared to have an exponential distribution, and the boxplot and (COOK) test were used to detect the outliers present in the real data. The Goodness of fit test was used for the one-parameter exponential model, and it was found that the data did not follow the normal distribution, and it was found that it suffers from the problem of heterogeneity of variance. The one-parameter exponential regression model for the expenditure and revenue data was estimated using the advanced search method because it was the best estimate. Paper type Research paper