With the expansion of HVDC grids, short-circuit faults and their protection issues are among the main challenges of these networks, which should be given more attention. This study presents an investigation of the DC side fault current in HVDC grids during the transient period. Also, a fast and robust protection algorithm is introduced that is essential for secure and appropriate HVDC grids operation. The Short-Time Fourier Transform (STFT) is applied to extract the frequency components of the fault current, and the time features of these components are utilized as the basis of the proposed algorithm. A four-terminal cable-based HVDC grid with bipolar configuration is modeled via EMTP, and a wide range of simulation scenarios are applied for various fault locations, fault impedances, and operation points. Furthermore, the algorithm thresholds are determined with the explicit procedure. Simulation results indicate that the proposed method is fast, selective, sensitive, and robust against AC-side fault, operating condition variations, fault distance, and fault direction. Also, it has an appropriate performance during high impedance faults.