The containment vessel of nuclear power plants, concrete structures near the furnaces and roller lines, and chimneys, are exposed to high temperatures (120 °C to 350 °C) for long term. Research on the compressive properties of concrete after short-term high temperatures (usually within 3 h) has been widely conducted, while that of concrete after sustained high temperatures is scarce. In this research, the effects of temperature (120 °C to 350 °C), heating duration (3 h to 32 h) and initial stress level (0.2 to 0.6, ratio of initial applied stress to compressive strength at room temperature) on the failure mode, compressive strength, peak strain and stress-strain relationship of concrete after sustained high temperatures were studied. The results show that with increasing temperature and heating duration, concrete compressive strength gradually decreases, while concrete peak strain gradually increases. At heating duration of 24 h, the properties of concrete have basically stabilised. Preloading helps the concrete to resist the adverse effects of high temperatures by inhibiting the dehydration of cement matrix and the cracking of interfacial transition zone. For concrete with preload, transient thermal strain and short-term creep at high temperatures could not be recovered after cooling, which causes a significant increase in the peak strain of concrete. A compressive stress-strain model for concrete with preload after sustained high temperatures was developed, which consists of pre-creep ascending segment, creep segment, post-creep ascending segment and descending segment. Comparison of the prediction results with the test results proves that the model has high accuracy.