The effects of an electric field along the [110] growth axis on the polarization properties of the interband transitions in a (110) quantum well are studied within a multiband effective-mass approximation. The transfer-matrix method is applied to coupled effective-mass equations in order to obtain the eigenenergies and eigenstates of holes under an electric field within a steplike approximation to the potential. The calculated results are shown for a ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$As quantum well grown on a (110) InP substrate in which the ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As well layer is strained due to a lattice mismatch to the substrate, while the lattice constant of the ${\mathrm{Al}}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$As barrier layer is matched to that of the substrate. In the absence of an electric field, the first hole level (\ensuremath{\nu}1) in a quantum well having a Ga content of x=0.58 and a well width of 80 \AA{} is proved to have a light-hole character, while the second level (\ensuremath{\nu}2) has a heavy-hole character, due to the effect of tensile strain. The calculated result of the electric-field dependence of the hole energy levels for this quantum well shows an anticrossing behavior between the \ensuremath{\nu}1 and \ensuremath{\nu}2 levels. The optical matrix element of the dipole transition between the first electron state (c1) and the \ensuremath{\nu}1 or \ensuremath{\nu}2 state shows an anomalous behavior in the electric-field dependence, related to the anticrossing: For linear polarization along the [110] growth axis, the optical matrix element for the c1-\ensuremath{\nu}1 transition suddenly decreases with increasing field, while that for the c1-\ensuremath{\nu}2 transition rises in the anticrossing region, representing character changes from light- to heavy-hole-like and vice versa; for polarization parallel to the (110) quantum well, the in-plane optical anisotropy is extremely enhanced to as much as 100% near the anticrossing.