We present a detailed theoretical description of wave propagation in an acoustic gradient-index system with cylindrical symmetry and demonstrate its potential numerically to control acoustic waves in different ways. The trajectory of acoustic wave within the system is derived by employing the theory of geometric acoustics, and the validity of the theoretical descriptions is verified numerically by using the finite element method simulation. The results show that by tailoring the distribution function of refractive index, the proposed system can yield tunable manipulation on acoustic waves, such as acoustic bending, trapping, and absorbing.