The main objective of this article is to examine the numerical efficiency of the gamma approximation technique , developed by Broemeling and Shaarawy (1988) , to estimate the error variance of the noise term of the second order moving average process. In order to achieve our main goal , six simulation studies are conducted with different variances and coefficients ; then proposed criteria are calculated. The inspection of the numerical results shows that the proposed approximation can efficiently estimate the noise variance  with very high precision for moderate and large time series lengths. In addition , the numerical results show that better results can be obtained if the error variance is small.