The phase-field (PF) model has been extensively used as a powerful numerical methodology for simulating microstructure evolutions in various materials. This study develops a three-dimensional PF model to simulate the lithium (Li) diffusion and the stress evolution in the positive electrode of the all-solid-state Li-ion battery which consists of LiCoO₂ (LCO) particles and a solid electrolyte. The PF model incorporates the Cahn-Hilliard equation which describes the Li diffusion and the Butler-Volmer equation to determine the Li-ion flux at the interface between LCO and the electrolyte. In order to calculate the stress evolutions in LCO particles and the solid electrolyte at a low computational cost, we employ the PF microelasticity theory for elastically inhomogeneous systems that employs the Fourier transform to solve the mechanical equilibrium equation and, therefore, is more computationally efficient than the finite element method. Using the PF model, the effect of the Li concentration-dependent elastic constants of LCO on the stress evolution in a LCO particle during charging and discharging processes was revealed.