J/psi and psi' production cross sections in fixed-target experiment is calc
ulated, considering the contributions from both color-singlet and color-oct
et mechanisms. The results are applied to the investigations of the J/psi s
uppression and the psi'/psi ratio problems in p-A collisions. The results a
gree with the experimental data as the (c (c) over bar)-nucleon absorption
cross sections sigma(abs)(8) approximate to 10mb for (c (c) over bar)(8) an
d sigma(abs)(1) approximate to 0mb for (c (c) over bar)(1). The model is fu
rther used to investigate A-h collisions when comover absorption mechanism
is also considered. It is found that the observed experiment data of J/psi
and psi'/psi ratio in S-U collisions and Pb-Pb collisions can not be explai
ned consistently within this model. The possibility of QGP formation in S-U
and Pb-Pb collisions is also discussed.