Sharp boundary inversion is a relatively difficult problem in magnetotelluric (MT) and other geophysical inversion, which has been studied by many researchers. We analyze the focusing inversion which is based on the minimum gradient support functional provided by Zhdanov, M. S. (2004), and introduce a diagonal gradient support into the objective function to improve the presentation of oblique geo-electrical interface. Certain models are designed to test this method in the paper. Compared with the results inversed by the focusing inversion without diagonal gradient support, the shape of oblique geo-electrical interface really displays better, this new algorithm is also proved to be stable and practical. Meanwhile, in order to improve the computing efficiency, reciprocity theorem is used to calculate sensitivity matrix, and regularized conjugate gradient method is introduced to solve the objective functional minimum.