  We present the most complete analysis of the penguin correction to the
extraction of the standard-model parameter sin(2\phi_1) from the B^0 -> J/psi
K_S decay up to leading power in 1/m_b and to next-to-leading order in
\alpha_s, \phi_1 being the weak phase, m_b the b quark mass, and \alpha_s the
strong coupling constant. The deviation \Delta S_{J/psi K_S} of the
mixing-induced CP asymmetry from sin(2\phi_1) and the direct CP asymmetry
A_{J/psi K_S} are both found to be of O(10^{-3}) in a formalism that combines
the QCD-improved factorization and perturbative QCD approaches. The above
results, different from those of O(10^{-4}) and of O(10^{-2}) obtained in the
previous calculations, provide an important standard-model reference for
verifying new physics from the B^0 -> J/psi K_S data.
