We have measured the changes in oxy-haemoglobin and deoxy-haemoglobin in the adult human brain during a brief finger tapping exercise using near-infrared spectroscopy (NIRS). The cerebral metabolic rate of oxygen (CMRO2) can be estimated from these NIRS data provided certain model assumptions. The change in CMRO2 is related to changes in the total haemoglobin concentration, deoxy-haemoglobin concentration and blood flow. As NIRS does not provide a measure of dynamic changes in blood flow during brain activation, we relied on a Windkessel model that relates dynamic blood volume and flow changes, which has been used previously for estimating CMRO2 from functional magnetic resonance imaging (fMRI) data. Because of the partial volume effect we are unable to quantify the absolute changes in the local brain haemoglobin concentrations with NIRS and thus are unable to obtain an estimate of the absolute CMRO2 change. An absolute estimate is also confounded by uncertainty in the flow-volume relationship. However, the ratio of the flow change to the CMRO2 change is relatively insensitive to these uncertainties. For the finger tapping task, we estimate a most probable flow-consumption ratio ranging from 1.5 to 3 in agreement with previous findings presented in the literature, although we cannot exclude the possibility that there is no CMRO2 change. The large range in the ratio arises from the large number of model parameters that must be estimated from the data. A more precise estimate of the flow-consumption ratio will require better estimates of the model parameters or flow information, as can be provided by combining NIRS with fMRI.