Single crystals of K4Cu(MoO4)(3) and nonmagnetic K4Zn(MoO4)(3) have been grown by the flux-growth method. K4Cu(MoO4)(3) can be described as a quantum quasi-1-d antiferromagnet with correlations between neighboring Cu2+ ions but no magnetic long-range ordering down to 0.4 K. Comparison of the structure and magnetic properties of isostructural A(4)Cu(MoO4)(3) (A = K, Rb) allows the isolation of the effects of low dimensionality from structural distortion along the Cu-O-Mo chains. The characteristic one-dimensional behavior is hence suppressed to lower the temperature in K4Cu(MoO4)(3) in comparison with that of the Rb analogue. For example, a broad peak in the specific heat is observed similar to 2.3 K at 0 T, which is consistent with the onset of the quantum spin liquid state.