Abstract We propose to use rich informations on the p p , p ¯ p total cross sections σ tot below N ( ∼ 10 GeV ) in order to predict the total cross section and ρ ratio at very high energies. Using the FESR as a constraint for high energy parameters, we search for the simultaneous best fit to the data points of σ tot and ρ ratio up to some energy (e.g., ISR, Tevatron) to determine the high-energy parameters. We then predict σ tot and ρ in the LHC and high-energy cosmic-ray regions. Using the data up to s = 1.8 TeV (Tevatron), we predict σ tot p p and ρ p p at the LHC energy ( s = 14 TeV ) as 106.3 ± 5.1 syst ± 2.4 stat mb and 0.126 ± 0.007 syst ± 0.004 stat , respectively. The predicted values of σ tot in terms of the same parameters are in good agreement with the cosmic-ray experimental data sample up to P lab ∼ 10 8 – 9 GeV by Block, Halzen, and Stanov.