  The su$(n)$ Lie algebraic structure of the Pegg-Barnett oscillator that
possesses a finite-dimensional number-state space is demonstrated. The
supersymmetric generalization of Pegg-Barnett oscillator is suggested. It is
shown that such a supersymmetric Pegg-Barnett oscillator may have some
potential applications, {\it e.g.}, the mass spectrum of the charged leptons.
