This paper considers strongly absolute stability of Lur'e-type discrete-time descriptor systems and proposes a strict LMI-based popov criterion. By constructing a Lur'e-type Lyapunov function, a new popov criterion is established for strongly absolute stability of Lur'e-type discrete-time descriptor systems. It is further shown that the Popov criterion leads to a less conservative robust stability analysis method for a class of uncertain linear discrete-time descriptor systems. Finally, numerical examples are given to illustrate the effectiveness of the obtained results.