Abstract: Using the weight coefficient method and real analysis techniques, we discussed the problems of constructing semi-discrete Hilbert-type inverse inequality with generalized homogeneous kernel, gave necessary and sufficient conditions for constructing such inequality,  the calculating formula of the best constant factor, and the  operator expression of the inequality.

Key words: semi-discrete Hilbert-type inverse inequality, generalized homogeneous kernel, construction theorem, necessary and sufficient conditions,  ,  , best constant factor, integral operator, discrete operator