[Purposes] This paper aims to study the pull-out bearing capacity of chemical bolts anchored in concrete and their corresponding theoretical calculation methods. [Methods] Based on the quadrilinear bond-slip constitutive model, the residual friction strength at the interface between chemical bolts and concrete was considered, and the bond stress process between bolts and concrete was analyzed. The analytical equation for predicting the load-displacement curve of chemical bolts in the tensile state was derived. At the same time, a direct pull-out test of chemical bolts was designed and conducted to verify the reliability of the theoretical method. [Findings] With the increase in the anchorage depth of chemical bolts, the failure mode of anchorage bodies gradually changes from complex failure (mixed failure) to a single failure in which the bolt is pulled off. Compared with the standard errors (SEs) between the results calculated based on the trilinear model commonly used in anchor rod calculation and measured data, the SEs between the results calculated based on the quadrilinear bond-slip model and measured data are smaller, indicating that the theoretical formula derived in this paper can more accurately reflect the trend of bolt load-displacement under pull-out load. [Conclusions] The research conclusion can provide a corresponding theoretical reference for the pull-out stress analysis of components anchored by chemical bolts.