The demand for internet service has always been on the rise especially with the advent of new technological devices and the current information age. In this study, the data showing internet bandwidth consumed daily for staff and students of the University of Benin was considered based on maximum demand. The internet bandwidth data was chronologically harvested for 370 days and used to predict internet bandwidth demand. Data was examined for stationary and model fitness using autocorrelation function (ACF) and partial autocorrelation function (PACF) tests. Several ARIMA models were considered for predicting the demand as well as an outlier detection approach and the data was split in two for training and testing the model. The training data consisted of 200 data points while the testing had 160 data points. The result obtained showed that there were 13 outliers present in the data and the seasonal ARIMA(0,0,2)(0,1,1)7 was most suited with the stationary R2 of 0.959, R2 value of 0.957, root mean square error (RMSE) of value of 15.296, mean absolute error(MAE) of 10.852 and the normalized Bayesian information criterion (NBIC) score of 5.731.