This paper considers Lur'e type descriptor systems (LDS). The concept of strongly absolute stability is defined for LDS and such a notion is a generalization of absolute stability for Lur'e type standard state-space systems (LSS). A reduced-order LSS is obtained by a standard coordinate transformation and it is shown that the strongly absolute stability of the LDS is equivalent to the absolute stability of the reduced-order LSS. By a generalized Lyapunov function, we derive an LMIs based strongly absolute stability criterion. Furthermore, we present the frequency-domain interpretation of the criterion, which shows that the criterion is a generalization of the classical circle criterion. Finally, numerical examples are given to illustrate the effectiveness of the obtained results.