Single-mode　waveguide　devices　are　necessary　in　photonic　integrated　circuits.　Previous　studies　on　the　singlemode　conditions　(SMCs)　of　the　thin　film　lithium　niobate　(TFLN)　either　only　focus　on　wire　waveguide,　or　lack　comprehensive　discussions　on　the　influence　of　the　rib　waveguide　with　different　cross-section　area　at　a　certain　height.　In　this　paper,　a　systematical　study　on　the　SMCs　of　rib　waveguide　based　on　TFLN　is　carried　out　by　using　finite　difference　method　(FDM).　By　comparing　the　effective　refractive　index　between　the　first-order　mode　in　the　central　rib　region　and　the　fundamental　mode　in　the　slab　waveguide,　and　the　fraction　of　the　mode　power　flux　between　the　TFLN　rib　region　and　the　whole　waveguide　region,　the　SMCs　in　the　central　rib　region　are　analyzed　in　terms　of　geometric　parameters　of　the　TFLN　rib　waveguide.　The　simulation　results　suggest　that　no　single　equation　could　meet　the　SMCs　of　different　waveguide　structures　simultaneously　in　a　small　TFLN　with　the　height　no　more　than　900　nm.　Ultimately,　new　approximate　expressions　as　functions　of　rib-waveguide　width　and　etching　depth　are　proposed　to　precisely　describe　the　single-mode　condition　at　these　dimensions.