Abstract: In this paper, the matrix product state (MPS) and density matrix renormalization group (DMRG) methods are employed to investigate the properties of three-flavor SU(3) lattice quantum chromodynamics (QCD) in 1+1 dimensions at zero temperature and finite density. The research involves the computation and analysis of chirality condensation and quark condensation as functions of chemical number density.The results show that both the chiral condensate and the diquark condensate exhibit oscillatory behaviors at high quark chemical potentials, and a second-order phase transition occurs with the increase of the quark chemical potential.