Fiber couplers usually take a lot of space on photonic integrated circuits due to the large mode-size mismatch between the waveguide and fiber, especially when a fiber with larger core is utilized, such as a few-mode fiber. We demonstrate experimentally that such challenge can be overcome by an ultra-compact mode-size converter with a footprint of only 10 µm. Our device expands TE0 and TE1 waveguide modes simultaneously from a 1-µm wide strip waveguide to an 18-µm wide slab on a 220-nm thick silicon-on-insulator, with calculated losses of 0.75 dB and 0.68 dB, respectively. The fabricated device has a measured insertion loss of 1.02 dB for TE0 mode and 1.59 dB for TE1 mode. By connecting the ultra-compact converter with diffraction grating couplers, higher-order modes in a few-mode fiber can be generated with a compact footprint on-chip.