  Direct $J/\psi$ and $\psi'$ production rates at Tevatron are calculated in
the $k_t$-factorization approach within the color-singlet model. In this
approach, the production rates are enhanced by a factor of 20 compared to the
naive collinear parton model. However, the theoretical predictions are still
below the experimental data by at least one order of magnitude. This means that
to explain charmonium productions at Tevatron, we still need to call for the
contributions from color-octet channels or other production mechanisms.
