We report the first measurement of absolute hadronic branching fractions of Λ_c^+ baryon at the Î Λ_c^+ Λ_c^- production threshold, in the 30 years since the Λ_c^+ discovery. In total, 12 Cabibbo-favored Λ_c^+ hadronic decay modes are analyzed with a double-tag technique, based on a sample of 567 pb⁻¹ of e⁺e⁻ collisions at √s̅ = 4.599 GeV recorded with the BESIII detector. A global least-squares fitter is utilized to improve the measured precision. Among the measurements for twelve Λ_c^+ decay modes, the branching fraction for Λ_c^+ → pK^- π^+ is determined to be (5.84 ± 0.27 ± 0.23)%, where the first uncertainty is statistical and the second is systematic. In addition, the measurements of the branching fractions of the other 11 Cabibbo-favored hadronic decay modes are significantly improved.