  In this paper, we discuss the prompt j/psi production at e^+e^- colliders via
color-singlet and color-octet production mechanisms. The color-singlet
production processes include 1) e^+e^- to J/\psi gg; 2) e^+e^- to J/\psi
c\bar{c}; 3) e^+e^- to q \bar q ggJ/\psi and e^+e^- to q \bar q g\chi_c
followed by \chi_c to J/\psi \gamma. The color-octet production processes
include 1) e^+e^- to J/\psi g; 2) e^+e^- to j/psi q\bar q. Of all these
production channels, we find that the color-octet contributions dominate over
the color-singlet contributions at any energy scales. At low energies
(\sqrt{s}< 20 GeV), the dominant channel is e^+e^- to J/\psi g whereas at high
energies e+e^- to j/psi q\bar q will take the leading part. We also find that
the energy spectrum for the color-octet j/psi production in process e^+e^- to
j/psi q\bar q is very soft, and the mean energy of the produced j/psi is only
about 10 GeV~ 20 GeV even at very high energies (e.g. at 1000 GeV). The
extraction of color-octet matrix elements from j/psi production in e^+e^-
collisions is also discussed.
