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Mode size converter enables to match two waveguides with different mode sizes. It has already become an indispensable component in modern integrated photonics. Here, we propose a strategy for implementing an on-chip mode size converter consisted of a gradient geometry metasurface and two cascaded waveguide tapers on the lithium-niobate-on-insulator platform. The metasurface, which is formed by a series of length-graded silica nanostrips embedded into LN waveguide, functions as focusing of incident wave and exaltation of conversion efficiency. A mode size converter that enables to match a fundamental TE 00 mode in a 10-μm-wide waveguide with that in a 0.8-μm-wide one was simulated to verify the feasibility of the strategy. We show that the device is not only compact with a length of 22.9 μm, but also shows an ultra-broad operation band as much as 1150 nm (from 1100 to 2250 nm), over which the conversion efficiency keeps >90 %. In addition, we show that the device has a good robustness to fabrication deviations. The strategy proposed here can be flexibly extended to other waveguide cross-section sizes and other guided modes. • A strategy is proposed for realizing an on-chip ultra-broadband mode size converter. • It uses gradient geometry metasurface and cascaded tapers on LNOI platform. • It is proved by simulating a device connecting a wide waveguide with a narrow one. • The device is valid for on-chip use and has an ultra-broad band as much as 1150 nm. • The strategy has a good scalability, the device has an excellent fabrication tolerance. [ABSTRACT FROM AUTHOR]