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We calculate the $D$-wave heavy quarkonium production at fixed targetexperiments under the NRQCD factorization formalism. We find that the coloroctet contributions are two orders of magnitude larger than color-singletcontributions if color-octet matrix elements are taken according to the NRQCDvelocity scaling rules. Within the theoretical uncertainties, the predictionfor the production rate of $2^{--}$ $D$-wave charmonium state agrees with thepreliminary result of E705 and other experiments. Searching for the $1^{--}$$D$-wave state $\psi(3770)$ is further suggested.Comment: 13pages, 4 PS figures, final vertion to appear in PR

D-wave heavy quarkonium production in fixed target experiments