Recent observations of the abundance distribution of heavy elements in metal-poor old stars suggest an existence of more than one r-process site, proposing a different site for the synthesis of light r-process nuclei. One model is the r-process nucleosynthesis in the supernova shock traveling through the He-rich shell of the pre-supernova star. In this scenario, the 14N from preceding CNO burning is converted to 18F, via the reaction 14N(Ì_å±,γ)18F and subsequent Ì_å_+-decay forms 18O, which then produces neutrons via 18O(Ì_å±,n) or 18O(Ì_å±,γ)22Ne(Ì_å±,n) reactions. The statistical model predicted that the 18F(Ì_å±,p)21Ne reaction can compete with the Ì_å_+-decay at high helium density and temperatures. Since 21Ne(Ì_å±,n) has a positive Q-value, it has been identified as a stronger neutron source than 22Ne(Ì_å±,n). Because no published data on the 18F(Ì_å±,p)21Ne reaction are available, we have measured the total cross sections of the 18F(Ì_å±,p)21Ne reaction in inverse kinematics and the time-reverse reaction, 21Ne(p,Ì_å±)18F. The results were compared with Hauser-Feshbach statistical model calculations. The astrophysical implications of the new experimental reaction rate are discussed.