Using J/ψ radiative decays from 9.0 billion J/ψ events collected by the BESIII detector, we search for di-muon decays of a CP-odd light Higgs boson (A0), predicted by many new physics models beyond the Standard Model, including the next-to-minimal supersymmetric Standard Model. No evidence for the CP-odd light Higgs production is found, and we set 90% confidence level upper limits on the product branching fraction B(J/ψ→γA0)×B(A0→μ+μ-) in the range of (1.2-778.0)×10-9 for 0.212≤mA0≤3.0 GeV/c2. The new measurement is a 6-7 times improvement over our previous measurement, and is also slightly better than the BABAR measurement in the low-mass region for tanβ=1. © 2022 authors. Published by the American Physical Society.