In order to deal with detail features of parameter curves and surfaces, one local interpolation type of geometric iterative approximation method with multiple weights is presented. Firstly, the initial data points are classified into two groups： interpolating points and noninterpolating points. For the interpolating points, different weights are distributed to the corresponding adjusting vectors. For the noninterpolating points, there is no adjust- ment. Then, the iteration matrix is given and the convergence is further analyzed. Finally, the method has been generalized to 3D surfaces. The results of numerical examples show that, the method can deal with detail features flexibly and the iteration errors are relatively small.