We investigate a unidirectional coupled chiral fiber grating (UCFG) with both helical refractive index (RI) and loss modulation. The two modulations form a π/2 phase difference in the fiber cross-sectional azimuth angle, which "breaks" the mode coupled reciprocity of the forward and backward propagation. The forward propagation fundamental mode coupling is forbidden, while the backward propagation fundamental mode is coupled to the vortex mode. A simulation model based on the beam propagation method (BPM) is utilized to confirm the unidirectional coupling. Using the coupled mode analysis, we find that the key to the coupling difference lies in the non-Hermitian coupling matrix. In addition, the UCFG design involving mixed modulation is also discussed. The UCFG demonstrates its potential as a passive vortex beam generator, filter, and detector, with a transmittance difference of up to 30 dB between the coupled and uncoupled vortex modes.