In this paper, we present one approach in finite-time stability analysis of continuous and discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties. The new integral inequality for continuous quadratic function with exponential weights and new finite sum inequality for discrete quadratic function with the power weights are derived. By using these inequalities and convenient continuous and discrete Lyapunov-Krasovskii-like functionals with exponential and power weights, respectively, some sufficient conditions of finite-time stability are obtained in form of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology.