The problem of finite-time stability for uncertain time-varying delay systems with non-linear perturbations and parametric uncertainties and switched time-delay systems is studied. New integral inequality with exponential function is proposed to solve the stability problem. By using a suitable form of Lyapunov–Krasovskii-like functional (LKLF) with exponential function, the integral inequality and estimations of LKLF in the initial and the current time, new delay-dependent and less conservative stability criteria have been derived in terms of linear matrix inequalities. The average dwell time approach is used to study the FTS of switched time-delay systems. Five numerical examples are given to show the effectiveness of the obtained results.