We demonstrate a 490-attosecond timing jitter (integration bandwidth: 10 kHz - 39.4 MHz) optical pulse train from a 78.7-MHz repetition rate, all-fiber soliton Er laser mode-locked by a fiber tapered carbon nanotube saturable absorber (ft-CNT-SA). To achieve this jitter performance, we searched for a net cavity dispersion condition where the Gordon-Haus jitter is minimized while maintaining stable soliton mode-locking. Our result shows that optical pulse trains with well below a femtosecond timing jitter can be generated from a self-starting and robust all-fiber laser operating at telecom wavelength. (C) 2013 Optical Society of America