Whether a spin-1/2 Fermi gas with strong repulsive interaction will become ferromagnetic is a long-standing problem in condensed matter physics. Recently this problem has been studied experimentally by Wolfgang Ketterle’s group in MIT (Science, 325, 1521 (2009)) using ultracold Fermi gases with large positive scattering length nearby a Feshbach resonance, and they claim that the Stoner ferromagnetic phase transition has been observed. However, it was later pointed out that the experiment evidence itself can hardly rule out the competing non-magnetic but strongly correlated state. The situation remains quite controversial, partly because there is very little theoretical understanding of the beyond mean-field correlation in cold Fermi gas nearby resonance. We take a variational wave function approach to address this problem, which reveals a significant correction to previous mean-field and perturbation results, due to short-range correlation and unitary interaction.