In this paper, we discuss some models to fit for cancer mortality data. The data had been collected as a table of age- and period-specific mortality data at the Japanese Ministry of Health and Welfare. (http://wwwdbtk.mhlw.go.jp/toukei/index.html) An age-period-cohort model as a Poisson regression model has been often used for the analysis of the cancer mortality data. However, since many parameters are usually needed in the model, the non-identifiability problem occurs. We assume that the cohort effects are random variables, so we can apply the mixed model, to these data. As a result, the number of parameters could be decreased, then we could solve non-identifiability problem.