Phase evolution of soliton and that of first-order sidebands in a fiber laser are investigated by using nonlinear Fourier transform (NFT). Development from dip-type sidebands to peak-type (Kelly) sidebands is presented. The phase relationship between the soliton and the sidebands calculated by the NFT are in good agreement with the average soliton theory. Our results suggest that NFT can be an effective tool for the analysis of laser pulses.