At present, the researches on 2D inversion of IP data mainly aim at the HD (high density) IP data, which is mainly due to the equivalent distances between neighboring poles during data collection. Under such a condition, the division of finite element grid is convenient and the forward and inverse operation is easy. In forward operation, the finite element grid is automatically divided according to the practical data, and dual-grid system is used. The finite element modeling with linear variation of conductivity within each block is done, and the error of modeling result can be modified. In inversion, the partial derivatives of the apparent resistivity with respect to model resistivity are calculated by means of the relationship between the source and receiver locations and Broyden's method. And it is solved by using the conjugate gradient method, in which the calculation precision is almost the same as that in the SVD method. Through inversing the modeling data and observed data, it is shown that the algorithms of this paper are workable.