ZZ distribution is suitable to describe the life variable of a type of storage products that rarely failbefore a given design life，and the proportion of failures has increased significantly after the design life. Based on aprogressive type-II censored sample，firstly using Taylor' s formula to transform the the nonlinear part of thelikelihood function into a linear expression，the likelihood equation is solvable，and the approximate maximumlikelihood estimation ( AMLE) of the parameter is given. Secondly，using the best linear unbiased estimation( BLUE) method，a general analytical expression of the parameter is given. At the same time，the expression formof the estimation is further simplified for two kinds of special progressive type-II censored sample and the requirednumber table is constructed for the convenience of use. Finally，a numerical comparison of the two methods isperformed，and the results show that the best linear unbiased estimation of ZZ distribution is better than theapproximate maximum likelihood estimation.