A key direction of the development of modern power systems is the application of a continuously increasing number of grid-forming power converters to provide various system services. One of the possible strategies for the implementation of grid-forming control is a control algorithm based on a virtual synchronous generator (VSG). However, at present, the problem of VSG operation under abnormal conditions associated with an increase in output current remains unsolved. Existing current saturation algorithms (CSAs) lead to the degradation of grid-forming properties during overcurrent limiting or reduce the possible range of current output. In this regard, this paper proposes to use the structure of modified current-controlled VSG (CC-VSG) instead of traditional voltage-controlled VSG. A current vector amplitude limiter is used to limit the output current in the CC-VSG structure. At the same time, the angle of the current reference vector continues to be regulated based on the emerging operating conditions due to the voltage feedback in the used VSG equations. The presented simulation results have shown that it was possible to achieve a wide operating range for the current phase from 0° to 180° in comparison with a traditional VSG algorithm. At the same time, the properties of the grid-forming inverter, such as power synchronization without phase-locked loop controller, voltage, and frequency control, are preserved. In addition, in order to avoid saturation of the voltage controller, it is proposed to use a simple algorithm of blocking and switching the reference signal from the setpoint to the current voltage level. Due to this structure, it was possible to prevent saturation of integrators in the control loops and to provide a guaranteed exit from the limiting mode. The results of adding this structure showed a five-second reduction in the overvoltage that occurs when it is absent. A comparison with conditional integration also showed that it prevented lock-up in the limiting mode. The results of experimental verification of the developed prototype of the inverter with CC-VSG control and CSA are also given, including a comparison with the serial model of the hybrid inverter. The results obtained showed that the developed algorithm excludes both the dead time and the load current loss when the external grid is disconnected. In addition, there is no tripping during overload, unlike a hybrid inverter.