The paper proposes an approach to improve the yield of Chrome (Cr) thin-film sputtering process of the black matrix (BM) in color filter manufacturing and to find the robust parameters of the process with multiple quality characteristics by using the Taguchi method combined with the grey relational analysis. The research considers the correlation between quality characteristics and applies the principal component analysis to eliminate the multiple co-linearity. The weights of the quality characteristics are determined by employing the entropy measurement method. Two quality characteristics and four control factors with three levels were selected. Based on the Taguchi quality design concept, a L9 orthogonal array table was chosen for the experiments. The confirmation experiment verifies the proposed grey-based Taguchi method has the ability to find out the optimal process parameters with multiple quality characteristics. Besides, manufacturing with the attained optimal process parameters can reduce the opportunities of repair and rework of Cr thin-film and raise the yield.