The continuation of magnetic field of magnetic object is studied, and a novel method based on integral equation method and singular value decomposition is presented. In the implementation of the new method, the magnetic object's structure only needs to be coarsely partitioned as some elements by integral equation method, thus a linear system of equations can be obtained with the magnetic field measurements at a large plane below the magnetic object. The system of equations can be solved regularly by the truncated singular value decomposition technique and the modified singular value decomposition technique based on singular value decomposition, then the 3D magnetic fields reconstruction the upward and downward continuation of the magnetic object's magnetic field are realized. The precision and reliability of the new method are higher than the conventional ones; especially, the difficulty of the upward continuation in certain ranges is surmounted.