  In this work, we investigate the possibility to realize inflation and strong
first order electroweak phase transitions(SFOEWPT) together with the relic
density explanation. We studied the usual Higgs-portal real singlet dark matter
model and the global U(1) breaking complex singlet model with the pseudoscalar
being dark matter candidate. We focus on higher dark matter parameter regions
due to the lower dark matter masses region are almost excluded by the current
direct detection experiments except that of the so-called ${\it Higgs~ funnel
~regime}$ with $m_{DM}\sim m_h/2$. In both models, the SFOEWPT can occur
through two-step where the magnitude of the Higgs-singlet quartic couplings can
account for the Higgs or singlet inflation. The usual Higgs-portal real singlet
dark matter model can not address the correct relic density together with the
explanation of inflation and SFOEWPT. With the complex singlet model, the
correct relic density can also be obtained simultaneously when the mixing angle
$0.1<\theta<0.2$ and the dark matter mass is $\sim800$ GeV.
