Two-three (2/3)-level dual-active-bridge (DAB) converter is a promising DC-DC converter for medium and high voltage applications. That is due to its advantages like high power density, galvanic isolation, and capability of withstanding higher voltage ratings compared to the two-level DAB converters.However, the open-circuit fault (OCF) is critical for the 2/3level DAB converters, resulting in various negative effects, e.g., DC bias, overshoot current, and capacitor voltage imbalance. To address these issues, it is necessary to develop fault diagnosis and fault-tolerant control strategies. This paper thus proposes a method to identify the faulty switch based on the dynamic characteristics when the OCF occurs. The midpoint voltages of the neutral-point-clamped (NPC) bridge arms are employed as the fault diagnosis signals, where the faulty switch can be identified accurately based on the mean values and duty cycles of the midpoint voltages. Subsequently, a fault-tolerant control scheme based on a complementary-switch-blocking (CSB) method is proposed. In this scheme, when the OCF occurs on one switch, the gate-driving signal of its complementary switch is blocked, and the OCF negative effects, e.g., DC bias, overshoot current, and unbalanced capacitor voltages, can be alleviated significantly. Furthermore, the power transfer capability of the 2/3-level DAB converters is enhanced with the proposed scheme compared to the traditional bypass-arm (BPA) method. Finally, experimental tests are carried out to verify the theoretical analysis.