In this article, we construct proper weight coefficients and use them to establish a Hardy-Hilbert-type inequality involving one partial sum. Based on this inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed. We also consider the equivalent forms and the operator expressions of the obtained inequalities. At the end of the paper, we demonstrate that more new Hardy-Hilbert-type inequalities can be derived from the special cases of the present results.