A　path-following　control　scheme　is　proposed　using　finite-time　convergence　line-of-sight　(FCL)　to　achieve　rapid　convergence　of　position　errors　for　an　unmanned　surface　vehicle　(USV).　FCL　combines　classical　line-of-sight　(LOS)　guidance　with　finite-time　stability　theory　to　ensure　that　the　position　of　the　USV　converges　to　the　reference　path　within　a　predetermined　finite　time.　Specifically,　a　USV　model　is　developed　to　analyze　target　tracking.　Moreover,　a　novel　cross-tracking　error　function　is　designed　with　hyperbolic　characteristics　for　FCL　through　an　analysis　of　the　relationship　between　convergence　speed　and　cross-tracking　error　function.　Further,　the　path-following　system　stability　with　FCL　and　finite-time　controllers　is　analyzed　to　indicate　the　smaller　value　of　the　upper　bound　of　the　system　convergence　time　by　comparisons.　Finally,　simulations　and　experiments　are　performed　to　verify　that　FCL　has　a　faster　convergence　speed　than　the　LOS　with　error　sign　function　(LS)　and　the　linear　cross-tracking　error　function　(LLCF),　and　a　wider　algorithm　parameter　tuning　range　compared　to　LS.