The question of phase measurement for a quantum oscillator using the quantum non-demolition principle (NDP), which does not need the use of the wave packet reduction postulate, is studied. It is shown that this approach is appropriate to introduce in a proper way the relevant observables for unlocalized (unsharp) measurement of quantum phase. Our analysis suggests that in contrast to other quantum-mechanical problems (e.g. The position and the momentum of a particle), the operator to represent the phase of a quantum field cannot be separated from the measurement process. Thus, the quantum phase operator must be defined for a corresponding measurement scheme. Moreover, it allows us to describe the time continuous process of quantum phase observations and also to study the stochastic dynamics of the oscillator under such measurement.