Direct force and time-resolved two-dimensional particle image velocimetry measurements were performed on a jellyfish-like ornithopter model, which consists of two anti-phase flapping wings in a side-by-side arrangement. The focus is to study the effect of the time asymmetric pitching motion on the propulsive performance of this kind of ornithopter in a hovering state. It was shown that the fast downstroke and slow upstroke pattern is superior to symmetric back and forth pitching. Namely, more thrust and less fluctuations in the side force can be achieved. In order to provide explanations for this observation, various analyzing techniques, including vortex identification and tracking, spectral analysis, velocity triple decomposition, and reduced-order representation, were taken for a systematical characterization of the flow field in the wake. The spatiotemporal evolution of leading-edge vortices shedding from the wingtip during the downstroke and upstroke stages, as well as their mutual interaction, was found to be one of the key factors to account for the role of time asymmetric pitching on the alternation of thrust generation. Moreover, the delay of the transition of the wake to a turbulent state was observed in the scenario of fast downstroke. This is expected to be beneficial for the improvement of the hovering stability of the ornithopter.