This paper provides a new goal-oriented (GO) method for reliability analysis of repairable systems with multiple fault modes. First, formulas of operators describing components with multiple fault modes are derived based on Markov process theory. Second, qualitative reliability analysis of such a system is conducted by combining the existing GO method with the Fussell–Vesely method. Third, this new method is applied in reliability analysis of a hydraulic transmission oil supply system. Finally, comparing the study results with fault tree analysis (FTA) and Monte Carlo simulation shows that this new GO method is suitable for reliability analysis of repairable systems with multiple fault modes.