This work proposed a new hybrid parameterless optimization algorithm named the grey cuckoo differential (GCD) algorithm, using the components of the grey wolf optimizer (GWO), cuckoo search (CS), and differential evolution (DE). By integrating the strengths of these three algorithms, the hybrid model aims to obtain a balance between the exploration phase as well as exploitation phase, leading to greater convergence speed and a higher quality of the solution. The performance of GCD has been evaluated using the CEC 2017 and CEC 2019 benchmarks. In addition, three-proton exchange membrane fuel cell (PEMFC) stack parameter extraction experiments were performed to verify the performance and accuracy of the GCD algorithm. The results of the GCD algorithm are compared with the improved artificial humming bird algorithm (IHBO), young double-slit experiment (YDSE), subtraction average-based optimizer (SABO), artificial colony differential evolution optimizer (ABCDE), jDE100 (winner of CEC 2019 competition) and others to demonstrate its effectiveness. The GCD algorithm showed the lowest sum of square error (SSE) based on the comparison result. Finally, the mean absolute error (MAE), mean square error (MSE), root mean squared error (RMSE) and Friedman and Wilcoxon’s statistical tests show the robustness of the GCD algorithm with respect to other competitive algorithms found in the literature.