In this paper, a 3D model is proposed for investigating the performance of HGMS filters. This filter consists of a matrix of iron rods arranged in a channel with a square cross-section and subjected to an external magnetic field. The flowing fluid is the amine solution which contains the FeS micro-particles. In the presented model, first, the capture performances of magnetic particles for 2D geometries are calculated numerically at various conditions using COMSOL Multiphysics software through finite element method. Using these results, a database of capture performance has been established for different speeds of the flow, diameters of the particle and arrangement of the rods. By use of the processing of this database, the capture performance of semi-sized particles for a 3D problem is calculated through the integration of captured particles along the length of the rods. Finally, the amount of total particles captured on the rod matrix is obtained for a group of particles with various diameters assuming Gaussian distribution. The results indicate that in HGMS filters, the particle capturing is directly related to the particle diameter but inversely depends on Reynolds number and the vertical distance between the rods. Also, at the same conditions, the filtration of the triangular arrangement of rods is greater than the rectangular arrangement. However, the performance difference of these two arrangements decreases with increase in the flow velocity or increase in the distance between the rods or decrease in the diameter of the particles. These results can be used to optimize the filtration of particles in the magnetic filters at different conditions.