Abstract: Physical calculations of reactor cores are fundamental for reactor core design and nuclear safety analysis. The second generation of core calculation theory and methods based on advanced component homogenization theory and modern coarse grid block methods are commonly used in reactor core physics calculations. However, due to the fact that the two-step method of component homogenization does not accurately provide the grid rod power, the modified two-step method of cell homogenization based on the pin-by-pin homogenization theory of core calculations has gradually become a research hot spot in core calculations. Compared with the two-step method of component homogenization, the pin-by-pin calculation scheme only carries out the homogenization calculation for each cell in the component, which preserves the non-uniformity of different cells in the component, reduces the approximation and assumption in the core calculation, and can calculate the core number more accurately, which is conducive to the safety analysis of the core. However, the SP3/GSP3 methods currently in common use for pin-by-pin calculations still suffer from limitations in balancing computational accuracy and efficiency. In this regard, this paper aims to establish a core calculation method named quasi-diffusion theory which considers both computational efficiency and computational accuracy. First, the 3D quasi-diffusion equation was derived and established from neutron transport theory. Unlike the traditional diffusion equation, the formulation of the quasi-diffusion equation did not introduce a first-order approximation for the neutron angular flux, and the concept of the Eddington factor was introduced to deal with the leakage term of the neutron transport equation. The 3D quasi-diffusion equation was then formulated. In addition, a numerical solution model for the quasi-diffusion equation was developed by referring to traditional numerical solutions of the diffusion equation such as the transverse integral equation and using the nonlinear iterative cross section method. Second, since the Eddington factor was the key parameter in solving the quasi-diffusion equation, the solution of the quasi-diffusion equation depends on whether the Eddington factor was exact or not. In this paper, the Eddington factor was regarded as the homogenization parameter similar to other small group sections. The solution was obtained using Serpent, a modified version of the Monte Carlo program. Finally, several cases including the whole core model and the color-set assembly model were employed to validate the method, and the results were compared with the traditional diffusion and Monte Carlo reference solutions. By comparing the numerical output results under each model, the results show that for reactor cores with complex structures and strong heterogeneity, the accuracy of quasi-diffusion calculations is significantly better than that of traditional diffusion calculations, and the computationally efficient of the two methods is similar. In summary, the quasi-diffusion equation approximation, as a nonlinear method to approximate the neutron transport equation, is a computationally efficient and accurate method. It has great promise for new core calculations with strong neutron anisotropy and complex neutron energy spectrum.