The current understanding of the Paleozoic petroleum system in Hudson Bay Basin remains far from complete due in no small part to the uncertainty in locally-calibrated generation and migration models underpinned with reliable source rock kinetic data. To improve the petroleum systems model, four representative immature organic-rich calcareous shales of Late Ordovician age from onshore outcrops surrounding the Hudson Bay were analysed to characterize their source rock generation kinetics. To constrain uncertainty due to laboratory measurement errors in kinetic parameter estimation, six heating rates were used in the pyrolysis experiments for each sample, resulting in 24 kinetic datasets that reduce uncertainty from both source rock heterogeneity and inherited laboratory measurement errors. Under the assumed geological time and geothermal framework, application of the kinetic models resulted in internally consistent generation histories, suggesting that the source rock started to generate oil when temperature reached 100 °C. It is likely where the maximum burial depth excessed 3000 m, the source rocks were in oil generation window with kerogen transformation ratio varying in a range between 52 and 78%. The modeled source rock maturity range from the immature outcrop samples is supported by bulk rock geochemistry data from cuttings of the source rock interval in offshore wells with high S1 peaks, large humps on the left shoulder on S2 curves, typical feature of FID pyrograms in the oil window. Comparison of the kinetic behavior of the samples in this study with those of typical marine Type I, Type II and Type IIS source rocks under laboratory condition and the assumed geological time/temperature framework suggests that kerogen converts to oil in a lower temperature range than those typical normal marine Type II source rock. We attribute the moderate sulfur content (likely high sulfoxide/thiophene ratio) and presence of kerogen component groups that are more prone to cleavage at low temperature as the cause for low temperature onset of hydrocarbon generation.