Creep performance is a crucial factor that must be considered in structural design. This paper aims to investigate the creep failure mode, creep strain, creep compliance, and other creep properties of bamboo scrimber under long-term tension in parallel-to-grain. To establish a general creep life prediction method for the full stress level of the bamboo scrimber, a multi-branch Kelvin–Voigt model, a generalized Maxwell model, and a creep finite element simulation were employed. The results showed that the creep strain curve of bamboo scrimber included the unsteady creep stage and the stable creep stage, but not the accelerated creep stage. When the stress ratio was less than 0.3, the residual strength decreased gradually. Below 70% of the ultimate load capacity, the creep characteristics of the bamboo scrimber were linear viscoelastic, and the creep compliance was generally independent of the load level. The creep finite element model of bamboo scrimber could accurately calculate the creep deformation of specimens. Based on this creep finite element model and creep failure rules, a life prediction model for the full stress level of bamboo scrimber was established, which could accurately predict the creep life. This paper provides theoretical guidance for the creep design of bamboo scrimber in engineering structures.