Magnetoacoustic tomography with magnetic induction (MAT-MI) is a noninvasive electrical conductivity imaging approach that measures ultrasound wave induced by magnetic stimulation, for reconstructing the distribution of electrical impedance in a biological tissue. Existing reconstruction algorithms for MAT-MI are based on the assumption that the acoustic properties in the tissue are homogeneous. However, the tissue in most parts of human body has heterogeneous acoustic properties, which leads to potential distortion and blurring of small buried objects in the impedance images. In this study, we proposed a new algorithm for MAT-MI to image the impedance distribution in tissues with inhomogeneous acoustic speed distributions. With a computer head model constructed from MR images of a human subject, a series of numerical simulation experiments were conducted. The present results indicate that the inhomogeneous acoustic properties of tissues in terms of speed variation can be incorporated in MAT-MI imaging.