The design problem of dynamic output feedback controller for a class of multi-delayed neutral systems has been considered. A criterion for the existence and asymptotic stability of such controller is derived via defining a new integral operator. The criterion is expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. One numerical example is given to illustrate the proposed design method. Numerical simulation shows that the new design method is valid.