We have measured the almost-pure incoherent scattering function of liquid and solid parahydrogen, using inelastic neutron scattering. The experiments were carried out on TOSCA, a time-of-flight, inverse-geometry, crystalanalyzer spectrometer, operating on the pulsed neutron source at ISIS (UK). The experiments have been planned taking advantage of the intrinsic incoherence introduced in the scattering process by the rotational transitions. The measured double-differential cross section gives a direct experimental access to the microscopic dynamics of condensed hydrogen. From the high-energy region of the spectrum, where the impulse approximation for the center of mass motion applies, we have been able to extract the translational mean kinetic energy. In the low-energy region, using the Gaussian approximation, we compare the experimental data in the liquid phase with the results of a model for the velocity autocorrelation function. The results are encouraging, but suggest further work.