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) $e^{+}{e}^{-}\to J/\psi \mathrm{gg}$, (2) $e^{+}{e}^{-}\to J/\psi c\overline{c}$, and (3) $e^{+}{e}^{-}\to q\overline{q}ggJ/\psi$ and $e^{+}{e}^{-}\to q\overline{q}g{\chi }_c$ followed by ${\chi }_c\to J/\psi \gamma$. The color-octet production processes include (1) $e^{+}{e}^{-}\to J/\psi g$ and (2) $e^{+}{e}^{-}\to J/\psi q\overline{q}$. Of all these production channels, we find that the color-octet contributions dominate over the color-singlet contributions at any energy scale. At low energies $(\sqrt{s}<20\mathrm{}$ GeV), the dominant channel is $e^{+}{e}^{-}\to J/\psi g$ whereas at high energies $e^{+}{e}^{-}\to J/\psi q\overline{q}$ will take the leading part. We also find that the energy spectrum for the color-octet $J/\psi$ production in process $e^{+}{e}^{-}\to J/\psi q\overline{q}$ is very soft, and the mean energy of the produced $J/\psi$ is only about 10 – 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.

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