The urgent need for the integration of large amounts of renewable energy sources has led to further developing and expanding high voltage direct current systems, especially for the multi-terminal high voltage DC (MT-HVDC) systems. But these systems are much vulnerable to DC faults because of the relatively lower impedance and higher fault current, an effective solution for MT-HVDC systems against DC faults is using a modular hybrid DC circuit breaker (DCCB). And the modular hybrid DCCB needs to have the ability about whole and partial breaker failure detection, however, existing breaker failure detection methods focus on the whole failure detection. Hence, this paper proposes a breaker failure detection method based on the transient power estimation which can detect the partial failure of the modular hybrid DCCB. The proposed method is as follows. First, the transient voltage and current across the modular hybrid DCCB is analyzed and the faulty feature between successful interruption situation and partial failure interruption situation is expressed when the MT-HVDC system occurs different faults. Second, the bus voltage, breaker voltage and line current are utilized to estimate transient power and a detection criterion based on the power error is constructed, Finally, many simulation experiments prove the effectiveness of the proposed method considering the different faulty resistances, faulty distances, faulty time, noise influence and the ageing of the metal-oxide varistor.