The electronic structure of the isolated [F(HF)₂]^- complex is calculated at the MP2/6-311++G(3df,3pd) level with the correction for the basis set superposition error taken into account. The equilibrium geometry of the complex is determined. Based on the four-dimensional (4D) potential energy and dipole moment surfaces calculated at this level of theory in the space of four variables describing the changes in the hydrogen bond lengths and the bond lengths of molecular subunits, the 4D anharmonic vibrational problem is solved by the variational method for the [F(LF)₂]^- (L = H, D, T) complexes. The vibrational energy levels, the transition frequencies and absolute intensities are determined for the three isotopomers. The conventional assignment of infrared absorption bands associated with the intramolecular stretches is improved. The isotope effect on the geometrical parameters of the [F(HF)₂]^- anion is studied by calculating the vibrationally averaged values of internuclear separations, their rms deviations, and the standard deviation of the H-bond asymmetry parameter for a number of vibrational states of the isotopomers. The vibrationally averaged values of the dipole moment are also computed.