In order to study the relationship between the pore structure of calcium based geopolymer and the compressive strength, on the basis of the data obtained from the nitrogen adsorption experiment, the grey system theory was used to analyze the impact of the pore structure parameters, the fractal dimensions and the distribution of aperture on the compressive strength and a prediction model for the 28d compressive strength was established. The results show that among the pore structure parameters, the pore specific surface area is positively associated with the compressive strength and causes the greatest influence on the compressive strength. Among the fractal dimensions, D3 is positively and most closely correlated with the compressive strength. Different aperture in different scopes is negatively correlated with the compressive strength, and the aperture of more than 100nm has the most significant impact on the 28d compressive strength of calcium based geopolymer. In the GM(1, 8) prediction model for the 28d compressive strength of calcium based geopolymer, the predictive value of strength is in accordance with the actual value with a high accuracy and the average relative error is 322 %.