  We present an analysis of the preliminary experimental data of direct j/psi
production in e^e- process at low energies. We find that the color-octet
contributions are crucially important to the cross section at this energy
region, and their inclusion produces a good description of the data. By fitting
to the data, we extract the individual values of two color-octet matrix
elements: <{\cal O}_8^{\psi}(^1S_0)> \approx 1.1\times 10^{-2} GeV^3, <{\cal
O}_8^{\psi}(^3P_0)> m_c^2\approx 7.4\times 10^{-3}GeV^3. We discuss the allowed
range of the two matrix elements constrained by the theoretical uncertainties.
We find that <{\cal O}_8^{\psi}(^1S_0)> is poorly determined because it is
sensitive to the variation of the choice of m_c, \alpha_s and <{\cal
O}_1^{\psi}(^3S_1)>. However <{\cal O}_8^{\psi}(^3P_0)> m_c^2 is quite stable
(about (6-9)\times 10^{-3}GeV^3) when the parameters vary in reasonable ranges.
The uncertainties due to large experimental errors are also discussed.
