Two-dimensional magnetotelluric (MT) inversion algorithm using minimum support (MS) stabilizer functional was implemented in this study to enhance the contrast of inverted images. For this implementation, this study derived a formula in discrete form for creeping model updates in the least-squares linearized inversion. A spatially varying regularization parameter determination algorithm, which is known as ACB (Active Constraint Balancing), was also adopted to stabilize the inversion process when using MS stabilizer as a model constraint. Inversion experiments for a simple isolated body model show well the feature of MS stabilizer in concentrating the anomalous body compared with the second-order derivative model constraint. This study also compared MS stabilizer and the second-order derivative model constraints for a model having multiple anomalous bodies to show the applicability of the algorithm into field data.