A new looped Lyapunov functional is employed to discuss the problem of the robust stability of aperiodically sampled-data control systems with communication delays. By taking full advantage of characteristic information on the whole sampling interval $[t_k,t_{k+1})$, a novel two-side time-dependent looped Lyapunov functional is presented. By using the proposed looped Lyapunov functional and the modified 3-order Bessel-Legendre inequality, some new robust stability criteria are established for the considered system. Several simulation examples show that the presented methods in this paper are less conservatism that some existing ones.