The first cause of death in the elderly is also cancer, and unfortunately, the percentage of such death in people over 65 years old is increasing with days. The statistics and analysis of the cause of death have become significant for planning of public health policies and improving the overall health of the people of Taiwan. Trend extension algorithm is often used for quantitative disease forecasting. One such model is the Autoregressive Integrated Moving Average (ARIMA) model. This model can be used to forecast time series data, especially for problems where random process characteristics change over time and causes the time series to be non-stationary and random. At present, most of the datasets on cancer mortality in various cities and counties in Taiwan belong to non-stationary and non-seasonal time-series data. They are suitable to use in the trend extension algorithm to forecast future trends. In order to further improve the forecast accuracy, the present study improved the traditional ARIMA algorithm. First, the cancer mortality data announced by the Ministry of Health and Welfare, Taiwan, for the past 26 years from 1992 to 2017 were divided into training and test data to compare the accuracy of different improved forecast algorithms. One of the forecasting performance evaluation methods is to estimate the forecast accuracy of each algorithm via Mean Absolute Percentage Error (MAPE). Finally, the best improved ARIMA algorithm was then used to forecast the cancer mortality in Taiwan for the next five years. The forecast results will provide the relevant government agencies with prior knowledge of the possible trends of cancer mortality and act as a reference for policy planning. These would allow people (especially the elderly) to receive appropriate cancer screening mechanisms, and those who already have cancer can get proper treatment, reduce cancer mortality, and improve their quality of life.