  Recently, a combined model of the primordial inflation and the present cosmic
acceleration has been proposed in the context of f(R) gravity. This model is
composed of the late-time acceleration term and an R2 term, which enables the
model to avoid high curvature singularity and describe a quasi-de Sitter
inflationary phase in the early Universe. An interesting feature of this model
is that the reheating dynamics after the inflation is significantly modified,
in contrast to the original R2 model, and affects the shape of a gravitational
wave background (GWB) spectrum. Here we investigate the production of a GWB
during the inflation and reheating eras in the R2-corrected f(R) model and
compute a GWB spectrum. We found that interesting region of the model
parameters has already been excluded by the cosmological limit on abundance of
GWs.
