A novel method named as VIM for microwave imaging of twodimensional dielectric cylinder in free space is presented. It is an iterative method based on volume equivalence principle and variation principle. The performance of it is examined throgh the reconstruction of many kinds of objects in the presence of random noise. Compared with the well known BIM

it inverts the unknown objects mor quickly and more accurately. It can rerenstruct the distribution of permttivity and conductivity simultanamsly. It is also shown that it can invert those complex objects such as multi-cylinder object

large object

high-contrast object. The behavior of this method in the case of incomplete scattering data is taken into account too. The effect of random noise and the capability of this method to invert unknowns using singe frequency scattering data are also investigated. We have also explained the reason why our method behaves better than the formr methods such as BIM and DBIM.