How to improve consensus conditions for double-integrator multi-agent systems is investigated. First, a consensus algorithm is presented and the corresponding convergence condition is described. However, the given convergence condition is conservative such that consensus is still obtained when the parameters of the consensus algorithm violate the given convergence condition. Second, to cope with this issue, a less conservative convergence condition is proposed by using complex number and matrix properties. Finally, simulation results illustrate the effectiveness of the convergence condition through two examples.