Maize in Canada is grown mainly in the south-eastern part of the country. No comprehensive studies on Canadian maize yield levels have been done so far to analyse the barriers of obtaining optimal yields associated with cultivar, environmental stress and agronomic management practices. The objective of the current study was to use a modelling approach to analyse the gaps between actual and potential (determined by cultivar, solar radiation and temperature without any other stresses) maize yields in Eastern Canada. The CSM–CERES–Maize model in DSSAT v4·6 was calibrated and evaluated with measured data of seven cultivars under different nitrogen (N) rates across four sites. The model was then used to simulate grain yield levels defined as: yield potential (YP), water-limited (YW, rainfed), and water- and N-limited yields with N rates 80 kg/ha (YW, N-80N) and 160 kg/ha (YW, N-160N). The options were assessed to further increase grain yield by analysing the yield gaps related to water and N deficiencies. The CSM–CERES–Maize model simulated the grain yields in the experiments well with normalized root-mean-squared errors <0·20. The model was able to capture yield variations associated with varying N rates, cultivar, soil type and inter-annual climate variability. The seven calibrated cultivars used in the experiments were divided into three grades according to their simulated YP: low, medium and high. The simulation results for the 30-year period from 1981 to 2010 showed that the average YP was 15 000 kg/ha for cultivars with high yield potential. The YP is generally about 6000 kg/ha greater than the actual yield (YA) at each experimental site in Eastern Canada. Two-thirds of this gap between YP and YA is probably associated with water stress, as a gap of approximately 4000 kg/ha between the YW and the YP was simulated. This gap may be reduced through crop management, such as introducing irrigation to improve the distribution of available water during the growing season. The simulated yields indicated a gap of about 3000 and 1000 kg/ha between YW and YW,N-80N for cultivars with high YP and low YP, respectively. The gap between YW and YW,N-160N decreased to <2000 kg/ha for high Yp cultivars with little difference for the low Yp cultivars. The different yield gaps among cultivars suggest that cultivars with high YP require high N rates but cultivars with low YP may need only low N rates.