A high-precision prediction method for calculating the ultimate bearing capacity of bolted joints of composite laminates based on different progressive failure criteria is studied. Based on the ABAQUS finite element software, the USDFLD subroutine is used for progressive failure analysis of the joints. Five failure criteria, namely the maximum stress criterion, Tsai-Hill criterion, Hoffman criterion, Tsai-Wu criterion, and Hasin criterion, are used for numerical calculation. Through the establishment of different field variables to characterize the damage state of the fiber, matrix, and interface, and then study the damage development process of the laminate bolted joint under tensile load, and verify the accuracy of the method by comparing with the test results. It is shown that the finite element simulation results calculated based on these five failure criteria are all close to the experimental values. Among them, the ultimate strength of the bolted laminates calculated by the Hasin criterion, which considers fiber failure and matrix failure separately, is the highest accuracy and most suitable for finite element simulation of composite bolted structure.