We report the first measurement of absolute hadronic branching fractions of Λ_{c}^{+} baryon at the Λ_{c}^{+}Λ[over ¯]_{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 sqrt[s]=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.