Lithium niobate-on-insulator (LNOI) has recently emerged as a promising material platform for high-density and advanced photonics integrated circuits (PICs). And single-mode waveguides (SMW) are the most basic building blocks for structuring various PICs. In this paper, single-mode conditions (SMCs) for shallowly etched LNOI rib waveguides in x-cut LNOI wafer are investigated with the finite element method (FEM) in consideration of the lateral leakage and the magic width for the first time, to our best knowledge. Our results indicate that due to the lateral leakage and the magic width these shallowly etched x-cut LNOI rib waveguides have unique and complex SMCs. Our method and results provide a guidance in designing low-loss LNOI SMW and high-performance PICs.