FinFET (Fin Field-Effect Transistor) technology is widely used in advanced transistor manufacturing process due to its lower leakage current, smaller short-channel effect, and lower power consumption. However, this special physical structure is very susceptible to manufacturing defects, which makes the FinFET memory prone to functional faults. Therefore, an efficient fault detection method is very important for the defect detection of FinFET memory. A detection algorithm called March FRD for FinFET memory faults is proposed in this paper. This paper summarizes the FinFET functional fault model, analyzes the corresponding coverage conditions, and verifies the correctness of the algorithm. March FRD performs well in detecting resistance dynamic faults, and its total fault coverage reaches 91.7%, which is significantly better than other existing March tests.