Abstract This paper studies the stability problem for linear systems with interval time-varying delay. By dividing the delay interval into two subintervals, delay-dependent exponential stability criterion and asymptotic stability criterion are obtained based on Lyapunov stability theory and reciprocally convex lemma. Furthermore, by assuming that the distribution of time delay is known, we allow that the derivative of Lyapunov–Krasovskii function have positive upper bound for the time delay in one subinterval, and get the delay distribution dependent stability criterion. We also extend the obtained criteria to the case that the delay interval is divided into more subintervals. The derived criteria are expressed in terms of Linear Matrix Inequalities (LMIs). Numerical examples are given to show the effectiveness of the proposed method.