An acoustic Luneburg lens is a symmetric gradient-index lens with a refractive index decreasing radially from the center to the outer surface. It can be used to manipulate acoustic wave propagation allowing collimation and focusing capabilities. Previously studied acoustic Luneburg lenses based on the conventional Luneburg lens concept work only at audible frequencies ranging up to 15 kHz or at a single ultrasonic frequency of 40 kHz. In this paper, by tailoring the focal length to be different from the length radius, a reduced-aberration acoustic Luneburg lens (RAALL) is proposed for broadband and omnidirectional acoustic collimation and focusing. Based on the ray trajectories obtained with the ray-tracing technique, the RAALL can achieve better acoustic focusing in comparison to a modified acoustic Luneburg lens based on the modified optical Luneburg lens design. Following this analysis, two models of RAALL [two-dimensional (2D) and three-dimensional (3D) devices] are designed and fabricated by using the additive manufacturing technology. Collimation and focusing performance of the ultrasonic waves are analytically, numerically, and experimentally investigated for both 2D and 3D lenses, and their broadband and omnidirectional characteristics are demonstrated.