Since the traditional definition of single-mode phase operator is not unitary, we attempt to identify a new definition. In view of the phase measurement is always relative to another reference phase, like the potential energy is always relative to zero-point position, we select to introduce phase operator in two-mode Fock space, which is the concrete way to propose a unitary two-mode phase operator operating on the two-mode entangled state representation. Its eigenvalue is just classical phase, and whose phase angle is the conjugate to photon-difference operator. We also present the number-difference-phase uncertainty relationship as well as Weyl-Wigner classical correspondence of the phase operator, which is the phase exp［iargtanp1+p1q1-q2］ in the two variable-pair coordinate-momentum space (q1,p1;q2,p2).