Integrated optical systems based on lithium niobate on insulator (LNOI) have attracted the interest of researchers. Recently, erbium-doped LNOI lasers have been realized. However, the reported lasers have a relatively lower conversion efficiency and only operate in the 1550 nm band. In this paper, we demonstrate an LNOI laser operating in the 1060 nm band based on a high Q factor ytterbium-doped LNOI microdisk cavity. The threshold and the conversion efficiency of the laser are 21.19 µW and 1.36%, respectively. To our knowledge, the conversion efficiency is the highest among the reported rare-earth-doped LNOI lasers. This research extends the operating band of LNOI lasers and shows the potential in realizing high-power LNOI lasers.