We discuss the one-dimensional Schrödinger equation for a harmonic oscillator with a finite step at the origin. The first half of this paper is a partial review of our recent work. In the latter half of this paper, we numerically compute the Wigner distribution function of the system and show several explicit examples. Our analyses confirm the negativity, as well as the anisotropy in the phase space, of the Wigner function of the system. A formula for the Wigner function is also provided in the cases where the eigenfunctions are piecewise analytic functions.