The nonlinear viscous element was introduced to study the creep process of recycled aggregate concrete. It was combined in series with the classic Burgers model to form a five-element six-parameter nonlinear creep model. Tensile creep tests were conducted on the recycled aggregate concrete with different fiber volume fractions and different replacement rates of recycled aggregate to investigate the variation of tensile creep compliance with loading time. Referring to the relationship between creep compliance and time in the creep model, the six mechanical parameters of the concrete's nonlinear creep model were identified through the optimization algorithm based on Levenberg-Marquardt. The fitting results of the model are consistent with the experimental results, indicating that the model can well reflect the creep characteristics of recycled aggregate concrete. It also shows that concrete with 0.12% volume fraction of recycled polypropylene fiber and 50% replacement rate of recycled aggregate has good economic practical value.