We propose a compact nanotube-mode-locked all-fiber laser that can simultaneously generate picosecond and femtosecond solitons at different wavelengths. The pulse durations of picosecond and femtosecond solitons are measured to be ∼10.6 ps and ∼466 fs, respectively. Numerical results agree well with the experimental observations and clearly reveal that the dynamic evolutions of the picosecond and femtosecond solitons are qualitatively distinct in the intracavity. Our study presents a simple, stable, low-cost, and dual-scale ultrafast-pulsed laser source suitable for practical applications in optical communications.