Cairns et al. [4]’s introduced a logistic regression in terms of two random walk processes  and  to modeling mortality-rate  as  For future research, they suggested to use the ARIMA class of time series models as an alternative to the random walk model. This article utilizes their suggestion and considers  and  as two time series  models in the above logistic regression model. Applications of the extended model explored for data collected, from 2004 to 2010, for post-age 60 males and females in Naghadeh, a town in the west Azarbaijan province in Iran, has been given. Using a developed an accuracy measure, this article concludes that the extended model provides more accurate prediction compares to the Cairns et al. [4]’s model. Several minor results have been given.