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¯→p¯π+ by using the process e+e-→J/ψ→ΛΛ¯. 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¯ averaged value of the decay parameter is extracted to be αavg=0.7542±0.0010±0.0024 with unprecedented accuracy. The CP asymmetry ACP=(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. © 2022 authors. Published by the American Physical Society.