This paper presents a Matlab-based program GCH.gravinv including an easy-to-use graphical user interface (GUI) for determining the depth to the basement of a sedimentary basin derived from inverting its gravity anomalies by an iterative procedure. The developed code uses an advanced iterative rapid algorithm based on the combination of the EFT-based algorithm of Granser and the space domain technique of Cordell and Henderson. As an advantage, this combination performs a fast computation with high precision and the inversion scheme does not require a mean depth or low-pass filtering. Given the required density contrast varying exponentially with depth and a pre-assigned criterion for the termination of the iterative procedure, the GUI allows the user an instant view of the convergence between the observed and inverted anomalies. The feasibility of the proposed algorithm is demonstrated on synthetic data from a 3D model where the obtained results coincide well with the actual depths. The inversion of a real gravity anomaly over Chintalapudi subbasin (India) is presented to compute the basement depths as a practical example. The obtained results from the real data application are in agreement with published information available for the study area.