Travel times and hence accessibility in urban areas are susceptible to traffic disruption caused by events such as congestion, roadworks and traffic accidents. Being highly valued by travellers, travel time reliability affects their participation in activities and thus, plays a decisive role in accessibility. The aim of the study was to develop an approach to integrate travel time reliability into the measurement of accessibility. To achieve this, we extended a commonly-used accessibility indicator to include day-today variability in travel times. In a case study of the accessibility to the newly-built Queen Elizabeth University Hospital (QEUH) in Glasgow, we used real-time travel times with high temporal resolution collected over a long period of time to demonstrate the applicability and the utility value of this approach compared to the standard accessibility measurement. Our results revealed that travel time reliability varied both temporally and spatially, and zones experienced relatively high levels of accessibility loss due to higher travel time variability. The proposed approach provides a more realistic representation of actual network performance, allows for assessing the effect of travel time reliability on accessibility throughout the day and will help transport planners to trace equity impacts on accessibility due to travel time unreliability.