Picosecond pulses have an important application in supercontinuum sources. A picosecond ytterbium-doped fiber laser passively mode-locked by an semiconductor saturable absorber mirror (SESAM) in linear cavity is constructed, and the effects of the reflectivity as well as the bandwidth of the fiber Bragg grating and the parameters of the SESAM on the characteristics of the output pulse are analyzed in detail and compared with each other. The experimental results show that a fiber Bragg grating with 10% reflectivity and 0.3 nm reflection bandwidth is more profitable for the mode-locking stability of the fiber laser, and the fiber laser has a wide working range for the parameters of the SESAM. In addition, the non-saturable loss of the SESAM has an important influence on the average output power of the fiber laser, and a smaller value of non-saturable loss results in higher output power for the laser.