Detection and quantification of circular RNAs (circRNAs) face several significant challenges, including high false discovery rate, uneven rRNA depletion and RNase R treatment efficiency, and underestimation of back-spliced junction reads. Here, we propose a novel algorithm, CIRIquant, for accurate circRNA quantification and differential expression analysis. By constructing pseudo-circular reference for re-alignment of RNA-seq reads and employing sophisticated statistical models to correct RNase R treatment biases, CIRIquant can provide more accurate expression values for circRNAs with significantly reduced false discovery rate. We further develop a one-stop differential expression analysis pipeline implementing two independent measures, which helps unveil the regulation of competitive splicing between circRNAs and their linear counterparts. We apply CIRIquant to RNA-seq datasets of hepatocellular carcinoma, and characterize two important groups of linear-circular switching and circular transcript usage switching events, which demonstrate the promising ability to explore extensive transcriptomic changes in liver tumorigenesis.