A search for CP violation with an entangled system of Ξ^{-}Ξ[over ¯]^{+} pairs is performed, using (10,087±44)×10^{6} J/ψ events collected with the BESIII experiment. A nine-dimensional helicity amplitude is used to fit e^{+}e^{-}→J/ψ→Ξ^{-}Ξ[over ¯]^{+} and its subsequent decays. The Ξ^{-} and Ξ[over ¯]^{+} decay parameters are determined with higher precision compared to the best results reported so far. Furthermore, the strong phase difference, (δ_{P}-δ_{S})=(0.3±1.2±0.2)×10^{-2} rad, and the weak phase difference, (ξ_{P}-ξ_{S})=(-0.2±1.2±0.1)×10^{-2} rad, are directly determined. These are the most precise measurements to date. The CP asymmetry observables A_{CP}^{Ξ}=(-7.8±4.8±0.8)×10^{-3} and Δϕ_{CP}^{Ξ}=(0.6±5.1±0.2)×10^{-3} rad are determined, which are consistent with CP conservation. In addition, independent measurements of the Λ decay parameter and CP asymmetry A_{CP}^{Λ}=(-2.9±4.3±0.7)×10^{-3} are also obtained, which are in agreement with the previous measurements, but with much improved precision.