The present paper gives the design of a new HGMS for magnetic separation of sulphides. The main characteristics of this HGMS are using iron-cladding saddle-shaped magnetic coil for instead of the ordinary magnet, and combining reciprocal-linear motion with vibration to actuate the separation box, and the magnetic field intensity is high up to 2T as well. For improving the magnet system design, a modified finite element method is used to calculate the distribution of magnetic field intensity of separation space of the magnetic coil, and accordingly the calculation results the magnetic leakage coefficient can be determined easily, thus designers apart from the empirical way. KEYWORDS: HGMS, reciprocal motion and vibration, finte element method, saddle-shaped coil.