We have developed a theory of the longitudinal g-factor of light holes in semiconductor quantum wells. It is shown that the absolute value of the light-hole g-factor can strongly exceed its value in the bulk and, moreover, the dependence of the Zeeman splitting on magnetic field becomes non-linear in relatively low fields. These effects are determined by the proximity of the ground light-hole subband, lh1, to the first excited heavy-hole subband, hh2, in GaAs/AlGaAs-type structures. The particular calculations are performed in the framework of Luttinger Hamiltonian taking into account both the magnetic field-induced mixing of lh1 and hh2 states and the mixing of these states at heterointerfaces, the latter caused by chemical bonds anisotropy. A theory of magneto-induced reflection and transmission of light through the quantum wells for the light-hole-to-electron absorption edge is also presented.