Abstract: Based on the established new-type exponential stability theorem for general retarded dynamical systems and two preliminary lemmas, less conservative stability conditions for linear systems with multiple time-varying delays are established by using the new stability analysis approach of Lyapunov function. Unlike some results in the literature, none of the established results depends on the derivatives of the time-varying delays. Therefore, the results are suitable to the cases with very fast time-varying delays. An example is provided to show that the stability conditions obtained are better than the ones obtained directly based on the standard Razumikhin-type condition in the literature.