In space geodetic and engineering construction, the transformation of different two-dimensional coordinates is often involved. The four parameter transformation model is usually used in the traditional coordinate transformation. In this paper, based on the Gauss Newton method, the two dimensional datum conversion joint model is transformed into a linear model, and then the fitting and estimating method is used to solve the model. The coordinate conversion is carried out by the seamless two dimensional datum conversion model, and the conversion between the conversion parameters and the non-public points is solved jointly. The simulation results show that the method is more accurate than the traditional two dimensional coordinate transformation model and the whole least square base conversion model