This paper focused on the stationary oscillation problems for delayed complex dynamical networks, with the full consideration of time delays in impulsive actions. With the help of inequality-based techniques, several novel sufficient conditions that guarantee the existence of stationary oscillations for error system between complex dynamical network and its isolated node were derived. Our presented method, unlike the existing results, demonstrated that such an error system can exhibit stationary oscillations under impulsive control strategies involving time delays, even when the system was initially divergent or unstable. Finally, two illustrative examples along with their simulation results were put forward for demonstrating the efficacy and effectiveness of the developed control method.