The absolute stability for a class of timevarying delay systems with sectorbounded nonlinearity was investigated. Based on the idea of delay decomposition, a new Lyapunov functional was constructed. By employing the freeweighting matrix combined with integral inequality approach, and considering the relationship between the timevarying delay and its upper bound, some delaydependent stability criteria were obtained and formulated in the form of linear matrix inequalities (LMIs). Finally, a numerical example was given to show that the effectiveness and superiorness over the existing ones.