Mapping the depth to basement from gravity anomalies is an essential geophysical survey in sedimentary basins. We propose an iterative method to simultaneously estimate the basement relief, exponential density-depth model, and constant offset. The iterative process is achieved by applying the approximate invariance, which directly relates the basement depth to density parameters and constant offset. The method can be employed provided that there are a few known depth constraints. By testing the sediment and basement models, we find that the observation plane height and random noise of gravity anomalies have almost no impact on the stability of the method. However, the method is slightly affected by the number of constraints and is sensitive to the uncertainty of constraint depth. Finally, we successfully use the new method to map the depth to basement in the Pannonian basin using several depth constraints from drilling data and obtain the almost same density-depth model as that assumed based on drilling density. The method can be extended to recover the discontinuous basement relief and estimate other density-depth models, such as polynomial density function, once appropriate adjustments are made to the method.