The physical characteristics and optical properties of PbS nanoclusters are investigated by using density functional theory (DFT) of first-principles. Microstructure models of (PbS)n (n=1-9) nanoclusters and bulk materials are built on Materials Studio platform, and its energy band structures, highest occupied molecular orbital-lowest unoccupied molecular orbital gap (HOMO-LUMO gap), density of state (DOS), and optical properties are calculated, respectively. Compared to PbS bulk materials, PbS nanoclusters show a discrete energy gap as well as the DOS, because of the quantum confinement effect. It is interesting that the HOMO-LUMO gap of (PbS)n (n=1-9) shows oscillates with the increasing of the n number. However, when its size is large enough, the HOMO-LUMO gap is gradually decrease with the increasing of size (>27 atoms). And, the HOMO-LUMO gap of PbS nanoclusters of different sizes is range from 2.575 to 0.58 eV, which covers the low loss communication band of optical communication. In addition, PbS nanomaterials (NMs) with small size are synthesized by using oleylamine as ligands. Sizes of PbS NMs can be accurately controlled through control of the reaction time as well as the growth temperature. The photoluminescence (PL) spectra show strong size dependence, which is large red shift with increasing size of the NMs. This trend is basically in agreement with the theoretical calculation above. Moreover, transmission electron microscopy (TEM) further reveals the morphology of PbS NMs. PbS NMs can be used in optical fiber amplifiers and fiber lasers because of its unique optical properties in optical communication bands.