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Texture evolution and inhomogeneous deformation of polycrystalline Cu during uniaxial compression are investigated at the grain scale by combining crystal plasticity finite element method (CPFEM) with particle swarm optimization (PSO) algorithm. The texture-based representative volume element (TBRVE) is used in the crystal plasticity finite element model, where a given number of crystallographic orientations are obtained by means of discretizing the orientation distribution function (ODF) based on electron backscattered diffraction (EBSD) experiment data. Three-dimensional grains with different morphologies are generated on the basis of Voronoi tessellation. The PSO algorithm plays a significant role in identifying the material parameters and saving computational time. The macroscopic stress–strain curve is predicted based on CPFEM, where the simulation results are in good agreement with the experimental ones. Therefore, CPFEM is a powerful candidate for capturing the texture evolution and clarifying the inhomogeneous plastic deformation of polycrystalline Cu. The simulation results indicate that the <110> fiber texture is generated finally with the progression of plastic deformation. The inhomogeneous distribution of rotation angles lays the foundation for the inhomogeneous deformation of polycrystalline Cu in terms of grain scale.