According to the theory of unit root test, Lee-Carter model and generalized linear model, which are widely used in mortality projection, impose key implicit assumptions respectively which are inconsistent with each other. Log mortality rate (the force of mortality or the central mortality rate) is described as a unit root process in Lee-Carter model, while it is modeled as a deterministic trend process in generalized linear model. We use panel LM unit-root tests with level shifts to test the assumptions in above models, based on mortality data of the 7 most developed countries(G7) and Nordic countries(Denmark, Finland, Norway, Sweden). The test results show that a mortality projection model, whatever it is Lee-Carter model or generalized linear model, is not always appropriate to predict dynamic mortality rates of different countries. Further, we explain period effect and cohort effect of dynamic mortality according to the results of structural break test. Based on the empirical results, we extend Lee-Carter model, which includes a special case of generalized linear model. To check the performance of the extended model, we use it to forecast USA and Sweden mortality and we find that the extended Lee-Carter model works better than the original Lee-Carter model.