By means of the emerging dispersive Fourier transform technique, we captured the pulse-resolved spectral evolution dynamics of double-pulse mode-locking in a single-walled carbon nanotube based Er-doped fiber laser from the initial fluctuations, monitoring the evolution process up to 10 s (corresponding to similar to 260 million roundtrips) discontinuously. Two distinctly different evolutionary types of double-pulse mode-locking have been investigated in detail: splitting from one pulse and forming simultaneously. Relaxation oscillations, beating dynamics, transient bound state, spectral broadening, and variation of pulse interval have been observed in the evolution processes of the double-pulse mode-locking. Our study will be helpful for the further research of double-pulse mode-locking.