Due　to　look-ahead　distance　(LAD)　is　not　adjusted　in　time　to　track　the　reference　trajectory　with　a　large　range　of　curvature,　and　unmanned　surface　vehicle　(USV)　tracks　the　trajectory　with　a　slow　convergence.　The　position　tracking　error　of　dynamic　systems　is　established　by　the　geometric　relationship　of　trajectory　tracking,　guidance　law　with　fast　finite　time　convergence　(FFTC-GL)　is　proposed　with　a　novel　time-varying　LAD　(NTLAD)　with　curvature　parameters　to　speed　trajectory　tracking.　FFTC-GL　includes　the　desired　heading　guidance　law　and　the　desired　cruise　speed　guidance　law.　Firstly,　NTLAD　function　is　solved　by　graphical　method　based　on　the　stability　constraints　of　NTLAD　to　realize　fast　finite　time　convergence　of　cross-error,　and　the　curvature　parameter　is　introduced　to　track　the　curve　trajectory　in　a　large　range　of　curvature.　Secondly,　the　fast　finite　time　speed　guidance　law　is　designed　by　the　finite　time　term　of　along-error　to　realize　the　finite　time　stability　of　along-error　dynamic　system.　Moreover,　the　upper　bound　of　the　convergence　time　is　deduced　for　FFTC-GL.　Finally,　simulations　of　the　trajectory　tracking　for　USV　indicate　that,　FFTC-GL　can　track　the　reference　trajectory　quickly　and　accurately,　both　for　straight　lines　and　curve　with　a　large　range　of　curvature.　©　2023　South　China　University　of　Technology.　All　rights　reserved.