Abstract: Magnetic induction tomography in biological tissues is a reconstruction method for complex conductivity distribution by measuring inductive voltage due to disturbances in an alternating magnetic field. A sensitivity matrix involves mapping changes of the conductivity distribution onto the induced voltage in a receiver coil. A method basad on finite element and compensation theary is presented for rapidly calculating the sensitivity matrix, and is applied to a variety of simulation experiments. Results indicate that a sensitivity matrix with single perturbation and multiple perturbations can be solved quickly using this method and thus it provides an effective means of image reconstruction of inverse problems in MIT.