We demonstrate a non-synchronous all-optical sampling system using a carbon-nanotube mode-locked laser with a tunable repetition-rate. This allows a stable and unambiguous waveform reconstruction without the inherent limitation encountered in conventional non-synchronous optical sampling such as the time-direction ambiguity and the frequency-hole or sparse-sampling phenomena. Real-time eye-diagram reconstruction of 160 Gbit/s return-to-zero (RZ) signals with sub-picosecond resolution and data-pattern recovery with sequence length up to 217 - 4 has be realized.