Based on 10 billion J/ψ events collected at the BESIII experiment, a search for CP violation in Λ decay is performed in the difference between CP-odd decay parameters α_{-} for Λ→pπ^{-} and α_{+} for Λ[over ¯]→p[over ¯]π^{+} by using the process e^{+}e^{-}→J/ψ→ΛΛ[over ¯]. With a five-dimensional fit to the full angular distributions of the daughter baryon, the most precise values for the decay parameters are determined to be α_{-}=0.7519±0.0036±0.0024 and α_{+}=-0.7559±0.0036±0.0030, respectively. The Λ and Λ[over ¯] averaged value of the decay parameter is extracted to be α_{avg}=0.7542±0.0010±0.0024 with unprecedented accuracy. The CP asymmetry A_{CP}=(α_{-}+α_{+})/(α_{-}-α_{+}) is determined to be -0.0025±0.0046±0.0012, which is one of the most precise measurements in the baryon sector. The reported results for the decay parameter will play an important role in the studies of the polarizations and CP violations for the strange, charmed and beauty baryons.