This paper introduces an improved stability criterion for discrete-time Lur’e systems with sector- and slope-restrictions. For the stability criterion, a Lur’e Lyapunov functional candidate is constructed to include quadratic terms and integration terms with nonlinearities. To handle the resulting integration terms in the Lyapunov difference, there is proposed a new bound lemma where the integration terms are relaxed into the second-order terms by the geometric point of view. In addition, an appropriate weighting method uses slack variables from the sector- and slope-restrictions. In the overall derivation, the stabilization condition is formulated in terms of a parameterized linear matrix inequality (PLMI), which is then converted into the linear matrix inequality. An example illustrates that the proposed criterion presents a less conservative result than the previous criteria in the literature.