Separation of magnetic catalyst particles from the wax stream in Fischer-Tropsch synthesis (FTS) process is one of the most important challenges for exploring FTS slurry bubble column reactors. In the present work, we studied the separation efficiency of magnetic catalytic particles from FTS wax using high gradient magnetic separation (HGMS), and the three-dimensional mathematical models were established to describe the magnetic field and magnetic force distribution with multi-wires for HGMS. The calculation results indicated that the distributions of magnetic field and magnetic force in HGMS were significantly related to the matrix arrangement patterns and the background uniform external magnetic field strength. The wire interval, the axial distance between matrices, the arrangement angle between matrices and the external magnetic field strength were investigated using the established models. Based on the experimental optimization, the magnetic iron content of the catalyst/wax mixture can be reduced to less than 30 ppm through HGMS, with the separation efficiency higher than 99.77% for iron particles. (C) 2013 Elsevier Ltd. All rights reserved.