We propose an all-fiber passively mode-locked laser emitting ± 1 order ultrafast optical vortex pulses with tunable wavelength and pulse-number, for the first time to the best of our knowledge. A home-made two-mode chirped fiber Bragg grating (TM-CFBG) is utilized to both select the higher-order mode and provide a relatively broad bandwidth to achieve ultrashort vortex pulses. The central wavelength of the vortex pulses can be tuned from 1552.23 nm to 1553.81 nm and the pulse duration reaches 6.31 ps. Through further simply controlling the cavity parameters, vortex pulses with different pulse-number are obtained as well. Moreover, the proposed laser exhibits pump hysteresis effect. This ultrafast vortex fiber laser with flexible tuning functions has potential applications in fields of optical communications, material processing, etc.