Arterial spin-labelled (ASL) MRI is used to quantify cerebral blood flow and arterial transit time. Currently, these parameters are not calculated at the scanner given the time-consuming processing required. Fast, automated parameter estimation is therefore desirable to radiology clinics. Here, we trained a convolutional neural network to estimate cerebral blood flow and arterial transit time from multiple post-label delay ASL. The network produces estimates comparable to other approaches and was designed to evaluate model uncertainty. This fast, automated method is suitable for scan-time generation of accurate hemodynamic maps, important in the assessment of neurological disorders and neurodegeneration.