  In this paper, we consider a reduced supersymmetric Yang-Mills integral with
four supercharges by using a Gaussian approximation scheme and its improved
version. We calculate the free energy and the expectation values of Polyakov
loop and Wilson loop operators by extending the method employed in the bosonic
case in the previous paper. Our results nicely match to the exact and the
numerical results obtained before. The loop amplitudes exhibit good scaling
behaviors similarly as in the bosonic case. The 't Hooft like large $N$ limit
leads simple formulas for the case of the loop length smaller. Also, the
Polyakov loop and the Wilson loop are computed for the case of the loop length
sufficiently large, where we see that the behavior of the Wilson loop
reproduces the result simulated for a few smaller values of $N$ at least
qualitatively.
