A modified version of the popular Lee-Carter method (Lee-Carter 1992) is applied to forecast mortality rates in Hungary for the period 2004–2040 on the basis of mortality data between 1949 and 2003 both for men and women. Another case is also considered based on a restricted data set corresponding to the period 1989–2003. The model fitted to the data of the period 1949–2003 forecasts increasing mortality rates for men between ages 45 and 55, pointing out that the Lee-Carter method is hardly applicable for countries where mortality rates exhibit trends as peculiar as in Hungary. However, models fitted to the data for the last 15 years both for men and women forecast decreasing trends similarly to the case of countries where the method was successfully applied. Hence one gets a better fit in this way, however, further concerns suggest that the Lee-Carter model, which is celebrated and widely used in actuarial practice, does not necessarily give sufficiently good prediction.