Abstract: In order to improve the convergence and stability of Euler inverted results, the iTilt-Euler method, which do not depend on the structure index, is used for the calculation. Furthermore, the data points are constrained by the peak values of tilt angle of the total horizontal derivative (TAHG) to optimize the solutions. The method has been demonstrated with synthetic and real data. For synthetic data, the convergence of iTilt-Euler inversion results constrained by the TAHG method is improved effectively to detect the fault structures with deeper depth. Application to gravity data for the ANZA basin in Kenya shows that the iTilt-Euler inversion results constrained by peak values of TAHG have good continuity. The results distribute generally along NW direction, followed by NE direction, and these characteristics are consistent with the identifying features of fault in the second-order vertical derivative and total horizontal derivative anomaly maps. Furthermore, the inversion depth results show that the solutions along NW direction are extend to large scale and with higher values, which is reflected as a basement fault that controls the boundary of the main tectonic units in the study area and usually cut by the superficial faults with NE extension. It is worth noting that a large deep fault with NNE extension is developed in the southeast of the study area, which cuts the north-west direction and the north-east direction fault. It is speculated that it may control the southeast boundary of the regional tectonic unit. We can conclude that the iTilt-Euler deconvolution combined with the peak constraint method can provide a reliable method for fault system interpretation, and has good practicability.