NOON states and M&M′ states are both typical path-entangled Fock state. M&M′ state is a new class of path-entangled photon Fock states which possesses photons in both path, and has been confirmed with a good performance in loss environment. In this paper, the detecting error-probability bound of quantum illumination based on M&M′ state was derived under the assumption that the target echo photons are pure states， which was also compared with the error-bounds of Fock state and NOON state. The simulation results show that the error bounds of M&M′ states are no longer limited by the total photon number, but influenced by the proportion of photon number between the signal path and the unused path. Therefore, the quantum illumination system with M&M′ states can offer an enhanced performance over Fock state in a larger dynamic range of signal to noise ratio(at least double time of NOON states).