Abstract B cells receptor (BCR) signaling in response to membrane-bound antigen increases with antigen affinity, a process known as affinity discrimination. However, if BCR molecules become signaling-capable immediately upon binding antigen, the decrease in serial engagement as affinity increases results in weaker signaling as affinity increases. We use computational modeling to show that a threshold time (kinetic proofreading) for antigen to stay bound to BCR before the latter becomes signaling-capable is needed to overcome the decrease in serial engagement with increasing antigen affinity, and replicate the monotonic increase in B cell signaling with affinity observed in experiments. This finding matches well with the experimentally observed timescale (~20 seconds) of antigen-mediated conformational changes to BCR that lead to Src-family kinase recruitment. The physical basis of the threshold time of antigen binding may lie in the formation timescale of BCR dimers. The latter decreases with increasing affinity, resulting in shorter threshold antigen binding times as affinity increases. Such an affinity-dependent kinetic proofreading requirement results in affinity discrimination very similar to that observed in experiments. We also develop a measure to characterize affinity discrimination in a quantitative manner. B cell affinity discrimination is critical to the process of affinity maturation, and thus our results have important implications in applications such as vaccine design.