Understanding a QCD phase structure is one of the ultimate goals of heavy-ion collision experiments.
Recent publications from the STAR Collaboration show a non-monotonic energy dependence of fourth-order fluctuations of net-proton, which could indicate a possible signature of the critical point at $\sqrt{s_{\rm{NN}}}\approx 7.7$ GeV.
The sixth-order fluctuations of net-proton multiplicity distributions were reported to be negative for central Au+Au collisions at $\sqrt{s_{\rm{NN}}}~=~200~$GeV.
This could suggest a smooth crossover transition at top RHIC energy.
In this paper, we present the results of higher-order fluctuations of net-proton up to the sixth-order from $p$+$p$ collisions at $\sqrt{s}~=~200~$GeV.
It provides precise physics baselines to be compared to Au+Au collisions.
The positive signs of the fifth- and sixth-order fluctuations in $p$+$p$ collisions are observed and their multiplicity dependencies are found to connect smoothly to those from Au+Au collisions.