The temporal and spatial variation characteristic of the temperature and relative humidity of early-aged concrete are dominant for the shrinkage cracking of early-aged concrete. The temperature and relative humidity interaction analysis model of early-aged concrete is present by the application of unconditional stable backward finite differential method. In the proposed model, the coupling effects of hydration, chemical drying and the diffusion of temperature and relative humidity are taken into account. The temporal and spatial variation of the relative humidity of early-aged concrete are simulated. The rationality of the proposed model is verified by the comparison with the test results. The parameters analysis have shown that the influence of temperature and humidity diffusion on relative humidity decreases with the distance from the diffusion surface. The influence of water-cement ratio on relative humidity is independent of position. The environmental humidity and surface moisture exchange coefficients primarily affect the relative humidity field near the concrete diffusion surface.