Luneburg lens is a gradient index lens that focuses the incoming wave to the opposite side of the lens without aberration. We developed a two-dimensional acoustic Luneburg lens by variable density method of space inside the lens. The lens is composed of hundreds of aluminum columns with various radii of less than 1cm. We tested the ability as sonar in the air. It focuses the incoming acoustic wave on the edge of the opposite side of the lens as well in the frequency range of 1,000Hz ~ 3,000Hz. It showed a dynamic response depending on the motion of the acoustic source. It could be a strong candidate of a next generation of sonar.