  We present the results of our analysis on charmonia ($J/\psi$ and $\psi'$)
hadroproduction taking into account higher-order QCD effects induced by
initial-state radiation in a Monte Carlo framework, with the colour-octet
mechanism implemented in the event generation. We find that those colour-octet
matrix elements extracted so far from Fermilab Tevatron data for both $J/\psi$
and $\psi'$ production have to be lowered significantly. We finally make
predictions for charmonia production at the LHC, presenting a code for a fast
simulation with PYTHIA based on the colour-octet model.
