We quantify the effect of internal-jugular vein function on intracranial venous haemodynamics, with particular attention paid to venous reflux and intracranial venous hypertension. Haemodynamics in the head and neck is quantified by computing the velocity, flow and pressure fields, and vessel cross-sectional area in all major arteries and veins. For the computations we use a global, closed-loop multi-scale mathematical model for the entire human circulation, recently developed by the first two authors. Validation of the model against in vitro and in vivo Magnetic Resonance Imaging (MRI) measurements have been reported elsewhere. Here, the circulation model is equipped with a sub-model for venous valves. For the study, in addition to a healthy control, we identify two venous-valve related conditions, namely valve incompetence and valve obstruction. A parametric study for subjects in the supine position is carried out for nine cases. It is found that valve function has a visible effect on intracranial venous haemodynamics, including dural sinuses and deep cerebral veins. In particular, valve obstruction causes venous reflux, redirection of flow and intracranial venous hypertension. The clinical implications of the findings are unknown, though they may relate to recent hypotheses linking some neurological conditions to extra-cranial venous anomalies.