  We calculate the $D$-wave heavy quarkonium production at fixed target
experiments under the NRQCD factorization formalism. We find that the color
octet contributions are two orders of magnitude larger than color-singlet
contributions if color-octet matrix elements are taken according to the NRQCD
velocity scaling rules. Within the theoretical uncertainties, the prediction
for the production rate of $2^{--}$ $D$-wave charmonium state agrees with the
preliminary result of E705 and other experiments. Searching for the $1^{--}$
$D$-wave state $\psi(3770)$ is further suggested.
