Three phosphates MPb4(PO4)(3) (M = K, Rb, Cs) have been synthesized by the high temperature melt method. The single-crystal X-ray structural analyses reveal that all of them belong to apatite-type phases and crystallize in the same space group, P6(3)/m (no. 176). They exhibit a three dimensional (3D) structure that is composed of two kinds of channels constructed by [Pb(1)O-6] and (PO4]. And the [Pb(2)vertical bar K(1)] [Pb(2)vertical bar Rb(1)1, [Pb(2)vertical bar Cs(1)]) atoms are located in the small channels. Detailed structural comparison indicates that the cations effect on the framework geometry is less obvious among the title compounds and the reported lead apatite-type phosphates, however, although MPb4(PO4)(3) (M = K, Rb, Cs) have the similar stoichiometry with MM'(4)(BO3)(3), the different coordination of the B and P atoms, as well as the cations effect make MPb4(PO4)(3) and MM'(4)(BO3)(3) crystallize in various space groups. The IR spectra were used to verify the validity of their structure. The TG-DSC analysis results indicate that KPb4(PO4)(3) and RbPb4(PO4)(3) melt congruently. The UV-Vis-NIR diffuse reflectance spectra indicate that they have no obvious absorption from 300 to 2500 nm. Optical properties as well as band structure calculations have been also performed based on density functional theory methods.