A widely tunable mode-locked all-fiberized Yb-doped fiber laser with near-transform-limited spectrum linewidth is used. It consists of a tunable fiber Bragg grating (TFBG) and a fiber-coupled LiNbO3 phase modulator (PM) in a linear cavity. The TFBG is used to achieve tunable emission wavelength, and the intracavity PM is used to achieve actively mode-locking operation. We have experimentally demonstrated that the laser-emitting wavelength can be tuned between 1,041 and 1,091 nm with power fluctuation less than 3 dB. The temporal width of the laser pulse is about 1 ns, and the pulses are near transform-limited with a spectral linewidth of 1.3 GHz. The results may find useful application in optical communication and optical measurement system.