Allele-specific protein-RNA binding is an essential aspect that may reveal functional genetic variants (GVs) mediating post-transcriptional regulation. Recently, genome-wide detection of in vivo binding of RNA-binding proteins is greatly facilitated by the enhanced crosslinking and immunoprecipitation (eCLIP) method. We developed a new computational approach, called BEAPR, to identify allele-specific binding (ASB) events in eCLIP-Seq data. BEAPR takes into account crosslinking-induced sequence propensity and variations between replicated experiments. Using simulated and actual data, we show that BEAPR largely outperforms often-used count analysis methods. Importantly, BEAPR overcomes the inherent overdispersion problem of these methods. Complemented by experimental validations, we demonstrate that the application of BEAPR to ENCODE eCLIP-Seq data of 154 proteins helps to predict functional GVs that alter splicing or mRNA abundance. Moreover, many GVs with ASB patterns have known disease relevance. Overall, BEAPR is an effective method that helps to address the outstanding challenge of functional interpretation of GVs.