Erbium-doped thin-film lithium niobate (TFLN) lasers have attracted great interest in recent years due to their compatibility with high-speed electro-optic (EO) modulation on the same platform. In this work, high-efficiency single-mode erbium-doped microring lasers with milliwatt output powers were demonstrated. Monolithic lithium niobate microring resonators using pulley-waveguide-coupling were fabricated by the photolithography assisted chemo-mechanical etching (PLACE) technique. The maximum single-mode laser power of 1.26 mW with the side-mode suppression ratio (SMSR) of 50 dB was achieved around the wavelength of 1562 nm, as well as the maximum laser slope efficiency of 2.51% and the minimum laser linewidth of 30 kHz. Besides, the lasing band was easily switched by the pulley-coupler with variable waveguide widths. The demonstrated milliwatt-level on-chip microlasers hold great promise as bright light sources for various integrated devices on the TFLN platform such as EO modulators and combs.