<p>In this paper, we study a Lotka-Volterra memory-based competition-diffusion model with spatial heterogeneity under homogeneous Dirichlet boundary conditions. Focusing on the joint effects of memory-based diffusion and spatial heterogeneity, we derive an explicit expression of the spatially nonconstant positive steady state by the implicit function theorem and the Lyapunov–Schmidt reduction method, and further analyze its local stability and the Hopf bifurcation through the eigenvalue distribution and bifurcation analysis. When the memory-based diffusion coefficients fall within certain regions, the spatially nonconstant positive steady state is always locally stable, without stability switches, for any time delay. However, with the increasing of memory diffusion, stability switches and the Hopf bifurcation around the steady state are induced by the time delay. The results show that the memory-based diffusion can cause the stability change and the Hopf bifurcation in the competition model, as contrast with the classic competition model.</p>