We study the single transverse-spin asymmetry for inclusive light-hadron productions in the proton-proton collision, p up arrow p -> hX (h = pi, K, eta), for the RHIC kinematics based on the twist-3 mechanism in the collinear factorization. The analysis includes all the contributions from the soft-gluon pole and the soft-fermion pole for the twist-3 quark-gluon correlation functions in the transversely polarized proton. After discussing the flavor decomposition and the P(T)-dependence of the asymmetry obtained in the previous analysis at the center-of-mass energy root S = 62.4 and 200 GeV, we will give a prediction for the asymmetry at root S = 500 GeV and also for the eta-meson production. We found slightly smaller asymmetry at root S = 500 GeV for pi(+/-,0) and K(+) compared with those at the lower energies. The asymmetry for the eta-meson turned out to be significantly larger than that for pi(0).