Abstract: This paper studied the separation of Tantalum & Niobium from the rough concentrate of a rich hafnium zirconium ore by HGMS(High Gradient Magnetic Separation). The magnetic field of HGMS was divided into hexagonal cells and the saparatoion was analyzed by "instantaneous snapshot" method. Two groups of eccentric ellipse are used to approximate the trapping regions of different particles in each unit, and the yield, recovery and grade of Tantalum-Niobium concentrate are determined by solving the critical value of eccentric ellipse on the x-axis. The comparison between numerical results and practical experiments indicated that:the numerical method basically reveals the capture law of high gradient magnetic separation.It may improve the separation efficiency although the range and time of real experiments are decreased, which may play a guiding role on the high gradient magnetic separation of tantalum-niobium ore and other weakly magnetic minerals.