The delay-time concept has been extensively applied in the field of maintenance. Unlike traditional maintenance policy only considers one-stage system failure process, the delay-time concept defines a two-stage system failure process: the normal stage from new to an initial defect and the following delay-time stage from this defective point to failure. Previous works using delay-time concept have mainly focused on single-component systems and multi-component systems with a series configuration, however, have not been applied to k-out-of-n systems. Therefore, this paper proposes a delay-time-based inspection model for k-out-of-n systems and study the optimal inspection interval that minimizes the long-term expected cost per unit time. Both exponential and non-exponential distributions for the time-to-defect of the components are considered. Numerical examples are presented to illustrate the effectiveness of the proposed model.