The 2-µm waveband is becoming an emerging window for next-generation high-speed optical communication. To enable on-chip high-speed data transmission, improving the signal-to-noise ratio (SNR) by suppressing the coupling loss of a silicon chip is critical. Here, we report grating couplers for TE and TM polarized light at the 2-µm waveband. With a single-step fully etched process on the 340 nm silicon-on-insulator (SOI) platform, the devices experimentally demonstrate high coupling efficiency of -4.0 dB and 1-dB bandwidth of 70 nm for the TE polarized light, while -4.5 dB coupling efficiency and 58 nm 1-dB bandwidth for the TM polarized light. For comprehensive performance, both of them are among the best grating couplers operating in the 2-µm waveband so far. We also demonstrate 81Gbps high-speed on-chip data transmission using pulse amplitude modulation 8-level (PAM-8) signals.