Based on a semiconductor saturable absorber mirror (SESAM), an all-normal-dispersion ring cavity, tunable, ytterbium-doped passively mode-locked fiber ring laser is reported. Pumped by a 976 nm semiconductor laser, when the pumping power is more than 16 dBm, the fiber laser can realize tunnable output from 1033 nm to 1069 nm smoothly at a repetition rate of 25.4 MHz, and a regularly rectangular spectrum is produced. The dependence of output power, bandwidth, and domain pulse-width on wavelength is analyzed in detail at a fixed pumping power. The experimental setup is compact and self-started. In addition, the output pulse, with a spectrum width of 1.745 nm and time domain width of 34.85 ps at 1064 nm, is compressed to 15.45 ps by using single-channel grating pairs.