This paper mainly studies the stability of linear systems with a periodical time-varying delay. An improved delay-segmentation-based non-continuous piecewise Lyapunov–Krasovskii (L–K) functional is proposed. In comparison with the currently available L–K functional, this functional incorporates more delay-segmentation-interval-related information. Additionally, it effectively eases the boundary constraints at each segment point. Consequently, a stability criterion with reduced conservativeness for linear time-delay systems is derived. Finally, two numerical examples and a single-area load frequency control system are given to validate the efficiency of the proposed approach.