Most drug molecules modulate multiple target proteins, leading either to therapeutic effects or unwanted side effects. Such target promiscuity partly contributes to high attrition rates and leads to wasted costs and time in the current drug discovery process, and makes the assessment of compound selectivity an important factor in drug development and repurposing efforts. Traditionally, selectivity of a compound is characterized in terms of its target activity profile (wide or narrow), which can be quantified using various statistical and information theoretic metrics. Even though the existing selectivity metrics are widely used for characterizing the overall selectivity of a compound, they fall short in quantifying how selective the compound is against a particular target protein (e.g., disease target of interest). We therefore extended the concept of compound selectivity towards target-specific selectivity, defined as the potency of a compound to bind to the particular protein in comparison to the other potential targets. We decompose the target-specific selectivity into two components: 1) the compound’s potency against the target of interest (absolute potency), and 2) the compound’s potency against the other targets (relative potency). The maximally selective compound-target pairs are then identified as a solution of a bi-objective optimization problem that simultaneously optimizes these two potency metrics. In computational experiments carried out using large-scale kinase inhibitor dataset, which represents a wide range of polypharmacological activities, we show how the optimization-based selectivity scoring offers a systematic approach to finding both potent and selective compounds against given kinase targets. Compared to the existing selectivity metrics, we show how the target-specific selectivity provides additional insights into the target selectivity and promiscuity of multi-targeting kinase inhibitors. Even though the selectivity score is shown to be relatively robust against both missing bioactivity values and the dataset size, we further developed a permutation-based procedure to calculate empirical p-values to assess the statistical significance of the observed selectivity of a compound-target pair in the given bioactivity dataset. We present several case studies that show how the target-specific selectivity can distinguish between highly selective and broadly-active kinase inhibitors, hence facilitating the discovery or repurposing of multi-targeting drugs.