For the conservatism of second-order multi-agent systems with time delay, there is still room for improvement of the Wirtinger-based inequality. In the process of stability analysis of multi-agent systems with time delay, the introduction of the second-order Bessel-Legendre inequality to amplify the integral term is smaller than the Wirtinger- based inequality. The second[1]order Bessel-Legendre inequa- lity is closer to the true value of the integral term. In addition, in order to derive less conservative stability conditions, a triple integral term is added when constructing the Lyapunov functional. However, Wirtinger-based inequality cannot direc- tly deal with the double integral term generated by the derivation of the triple integral. Therefore, the Wirtinger- based double integral inequality is introduced to solve this problem. Based on Lyapunov stability theorem and linear matrix inequality theory, the stability conditions that ensure the multi-agent agreement and less conservative are obtained.