We present the acoustic band gaps (ABGs) for a geometry of three-dimensional complex acoustic crystals: the NaCl-type structure. By using the super cell method based on the plane-wave expansion method (PWE), we study the three configurations formed by water objects (either a sphere of different sizes or a cube) located at the vertices of simple cubic (SC) lattice and surrounded by mercury background. The numerical results show that ABGs larger than the original SC structure for all the three configurations can be obtained by adjusting the length-diameter ratio of adjacent objects but keeping the filling fraction (f=0.25) of the unit cell unchanged. We also compare our results with that of 3D solid composites and find that the ABGs in liquid composites are insensitive to the shapes as that in the solid composites. We further prove that the decrease of the translation group symmetry is more efficient in creating the ABGs in 3D water-mercury systems.