An acoustic focusing lens based on a coiling-up space structure with near-zero refractive index is studied. According to the direction selection mechanism for acoustic waves in a near-zero refractive index material, we adopt the coiling-up space structure as a basic unit for arrangement, and design a geometric structure with specific incident and outgoing interfaces which is used to manipulate the outgoing direction of transmitted wave. Thus, the focusing effects for plane acoustic wave and cylindrical acoustic wave are realized. Besides, the influences of rigid scatterers inside the lens on the focusing performance are also discussed in detail. Moreover, the shape and direction of the acoustic waveform can be manipulated accurately by changing the outgoing interface of the lens with the near-zero refractive index. The results show that the lens with a single and two circular surfaces could realize the focusing effects of the plane and cylindrical acoustic waves, respectively, and the rigid scatterers inside the lens have no effects on the focusing performance. In addition, the cylindrical acoustic wave could be transformed into the plane acoustic wave through the lens with the circular incident surface and the plane exit surface, and the inclined angle of the exit surface could be used to manipulate the propagation direction of the plane wave. The simulation results between the lenses composed of the coiling-up space structure and the effective medium are in good agreement with each other. This type of lens has the advantages of single cell structure, high focusing performance, and high robustness. This work provides theoretical guidance and experimental reference for designing a novel acoustic focusing lens with the near-zero refractive index, and offers a new idea for studying the manipulation of the acoustic waveforms.