Abstract Quasi-elastic incoherent neutron scattering experiments on glass-forming propylene carbonate are reported. Propylene carbonate can be regarded as a model material for studies of the dynamics around the glass transition due to its simple molecular structure and its extreme ‘fragility’ according to Angell's classification system. A broad quasi-elastic line is present in the spectra at high temperatures which rapidly narrows and increases in intensity when approaching the glass transition. The observations are attributed to the structural α-relaxation. A power law fits the temperature dependence of the structural relaxation time with an exponent of 2.3. The critical temperature obtained from the power law fit lies about 30 K above the calorimetric glass transition and is in fair agreement with that obtained from viscosity data. This observation as well as the temperature dependence of the non-ergodicity parameter are in overall accordance with the general predictions of the mode coupling theory.