MOTIVATION: Longer reads produced by PacBio or Oxford Nanopore sequencers could more frequently span the breakpoints of structural variations (SVs) than shorter reads. Therefore, existing long-read mapping methods often generate wrong alignments and variant calls. Compared to deletions and insertions, inversion events are more difficult to be detected since the anchors in inversion regions are nonlinear to those in SV-free regions. To address this issue, this study presents a novel long-read mapping algorithm (named as invMap). RESULTS: For each long noisy read, invMap first locates the aligned region with a specifically designed scoring method for chaining, then checks the remaining anchors in the aligned region to discover potential inversions. We benchmark invMap on simulated datasets across different genomes and sequencing coverages, experimental results demonstrate that invMap is more accurate to locate aligned regions and call SVs for inversions than the competing methods. The real human genome sequencing dataset of NA12878 illustrates that invMap can effectively find more candidate variant calls for inversions than the competing methods. AVAILABILITY AND IMPLEMENTATION: The invMap software is available at https://github.com/zhang134/invMap.git.