Lighter-than-air vehicles or blimps, are an evolving platform in robotics with several beneficial properties such as energy efficiency, collision resistance, and ability to work in close proximity to human users. While existing blimp designs have mainly used propeller-based propulsion, we focus our attention to an alternate locomotion method, flapping wings. Specifically, this paper introduces a flapping-wing blimp inspired by manta rays, in contrast to existing research on flapping-wing vehicles that draw inspiration from insects or birds. We present the overall design and control scheme of the blimp as well as the analysis on how the wing performs. The effects of wing shape and flapping characteristics on the thrust generation are studied experimentally. We also demonstrate that the flapping-wing blimp has a significant range advantage over a propeller-based system.