  We study the spontaneous R-symmetry breaking model and investigate the
cosmological constraints on this model due to the pseudo Nambu-Goldstone boson,
R-axion. We consider the R-axion which has relatively heavy mass in order to
complement our previous work. In this regime, model parameters, R-axions mass
and R-symmetry breaking scale, are constrained by Big Bang Nucleosynthesis and
overproduction of the gravitino produced from R-axion decay and thermal plasma.
We find that the allowed parameter space is very small for high reheating
temperature. For low reheating temperature, the U(1)_R breaking scale f_a is
constrained as f_a<10^{12-14}GeV regardless of the value of R-axion mass.
