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We theoretically investigate the phase sensitivity with parity measurement on a Mach-Zehnder interferometer with a coherent state combined with a squeezed number state.Within a constraint on the total mean photon number,we find,via parity measurement,that the mixing of a coherent state and squeezed number state can give better phase sensitivity than mixing a coherent state and squeezed vacuum state when the phase shift deviates from the optimal phase φ =0.In addition,we show that the classical Fisher information for parity measurement saturates the quantum Fisher information when the phase shift approaches to zero.Thus,the quantum Cramér-Rao bound can be reached via the parity measurement in the case of φ =0.