  The oscillator algebra of Pegg-Barnett (P-B) oscillator with a
finite-dimensional number-state space is investigated in this note. It is shown
that the Pegg-Barnett oscillator possesses the su($n$) Lie algebraic structure.
Additionally, we suggest a so-called supersymmetric P-B oscillator and discuss
the related topics such as the algebraic structure and particle occupation
number of supersymmetric P-B oscillator.
