The methodology of designing traveling-wave series-fed patch array antennas (TSPAAs) based on reflection-canceling elements for flexible radiation pattern has been proposed. By introducing a quarterwave transformer as the reflection-canceling structure, the cascaded patch antenna with tapered width can be used as the reflection-canceling element for a nonuniformly spaced TSPAA. Because of its simple structure, the parameters of the transformer can be determined directly by the corresponding equivalent circuit. To achieve a flexible radiation pattern, the array aperture distribution can be controlled by changing the element width (for amplitude distribution) and the element spacing (for phase distribution). In this method, the initial array is synthesized through a genetic algorithm approach, and a simulation-based iterative process considering the accurate mutual coupling is developed to optimize the initial array. To evaluate the proposed method, two different types of 14-element linear arrays operating at ISM 24GHz are implemented for a low sidelobe pattern and shaped-beam pattern, respectively. The two arrays are both simulated, fabricated and measured, the measured results show reasonable agreement with the simulation results, which verifies the effectiveness and correctness of the proposed method in this paper.INDEX TERMS Genetic algorithm (GA), low sidelobe pattern, reflection-canceling element, simulationbased iteration procedure, shaped-beam pattern, traveling-wave series-fed patch array antenna (TSPAA).