<p>In this paper, we investigate the Hopf-Hopf bifurcation in the memory-based diffusion system with nonlocal effect. By treating the memory delay and the memory-based diffusion coefficient as bifurcation parameters, we develop an algorithm to compute the normal form for the codimension-two non-resonant or weakly resonant Hopf-Hopf bifurcation of this system. To demonstrate the effectiveness of the proposed algorithm, we consider a real memory-based diffusive predator–prey system with a Holling type-III functional response and nonlocal effect. For this system, we first perform a Hopf-Hopf bifurcation analysis, and then, using the developed algorithm, we explore the dynamical classification near the Hopf-Hopf bifurcation point. Through numerical simulations, we observe the emergence of stable periodic solutions as well as a stable positive constant steady state.</p>