Based on the solidification theory, an recursion format for calculating concrete creep is derived. The recursion process can be programmed by commercial finite element software. Firstly, the creep Volterra integral equation was transformed into a rate-type creep integrodifferential equation based on the Kelvin chain model; secondly, the integrodifferential equation was transformed into a recursive creep calculation equation by discretizing the time and introducing intermediate variables; thirdly, a stress-strain incremental elastic constitutive relationship with initial strain was established by using the recursive calculation. The stress-strain incremental elastic constitutive relationship was suitable for complex stress conditions. Finally, as an application, the Ansys finite element commercial software was re-developed by modifying the material constitutive subroutine Usermat with Fortran language. Some existing examples were calculated by the program. The calculation results show that proposed method has satisfactory accuracy by comparing with the existing results. The proposed method does not need to store the stress history, which greatly improves the calculation efficiency, and also provides another effective way for the creep calculation of complex concrete structure.