This paper is aimed at presenting a technique appraising software trustworthiness grounded on Grey correlation analysis, which performs calculating of the weight for each index by virtue of trapezoidal fuzzy number. This paper initially works out at positive and negative ideal values for trustworthiness indicators, whereby to figure out the Grey correlation degree concerning the index value and the ideal value whereof. Grounded on this, the paper estimates the value for software trustworthiness and the empirical evidence reveals that the specified methodology is of validity and accuracy. Hence, this technique can be applied into more studies on software trustworthiness.