A narrow structure in the pΛ[over ¯] system near the mass threshold, named as X(2085), is observed in the process e^{+}e^{-}→pK^{-}Λ[over ¯] with a statistical significance greater than 20σ. Its spin and parity are determined for the first time to be J^{P}=1^{+} in an amplitude analysis, with a statistical significance greater than 5σ over other quantum numbers (0^{-},1^{-} and 2^{+}). The pole positions of X(2085) are measured to be M_{pole}=(2084_{-2}^{+4}±9) MeV and Γ_{pole}=(58_{-3}^{+4}±25) MeV, where the first uncertainties are statistical and the second ones are systematic. The analysis is based on the study of the process e^{+}e^{-}→pK^{-}Λ[over ¯] and uses the data samples collected with the BESIII detector at the center-of-mass energies sqrt[s]=4.008, 4.178, 4.226, 4.258, 4.416, and 4.682 GeV with a total integrated luminosity of 8.35 fb^{-1}.