With the advent of RNA-sequencing technology, we can detect different types of alternative splicing and determine how DNA variation regulates splicing. However, given the short read lengths used in most population-based RNA-sequencing experiments, quantifying transcripts accurately remains a challenge. Here we present a method, Altrans, for discovery of alternative splicing quantitative trait loci (asQTLs). To assess the performance of Altrans, we compared it to Cufflinks and MISO in simulations and Cufflinks for asQTL discovery. Simulations show that in the presence of unannotated transcripts, Altrans performs better in quantifications than Cufflinks and MISO. We have applied Altrans and Cufflinks to the Geuvadis dataset, which comprises samples from European and African populations, and discovered (FDR = 1%) 1,427 and 166 asQTLs with Altrans and 1,737 and 304 asQTLs with Cufflinks for Europeans and Africans, respectively. We show that, by discovering a set of asQTLs in a smaller subset of European samples and replicating these in the remaining larger subset of Europeans, both methods achieve similar replication levels (95% for both methods). We find many Altrans-specific asQTLs, which replicate to a high degree (93%). This is mainly due to junctions absent from the annotations and hence not tested with Cufflinks. The asQTLs are significantly enriched for biochemically active regions of the genome, functional marks, and variants in splicing regions, highlighting their biological relevance. We present an approach for discovering asQTLs that is a more direct assessment of splicing compared to other methods and is complementary to other transcript quantification methods.