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By means of the nuclear parton distributions determined without the fixed-target Drell-Yan experimental data and the analytic expression of quenching weight based on BDMPS formalism, a next-to-leading order analyses are performed on the Drell-Yan differential cross section ratios from Fermilab E906 and E866 Collaborations. It is found that the calculated results with only the nuclear effects of parton distribution are not in agreement with the E866 and E906 experimental data. The incoming parton energy loss effect can not be ignored in the nuclear Drell-Yan reactions. The predicted results indicate that with the quark transport coefficient as a constant, the suppression due to the target nuclear geometry effect is approximately 19.24% for the quark transport coefficient. It is shown that we should consider the target nuclear geometry effect in studying the Drell-Yan reaction on nuclear targets. On the basis of Bjorken variable and scale dependence of the quark transport coefficient, the atomic mass dependence is incorporated. The quark transport coefficient is determined as a function of the atomic mass, Bjorken variable $x_2$ and scale $Q^2$ by the global fit of the experimental data. The determined constant factor $\hat{q}_0$ of the quark transport coefficient is $0.061\pm0.004 {\rm GeV^2/fm}$. It is found that the atomic mass dependence has a remarkable impact on the constant factor $\hat{q}_0$ in the quark transport coefficient in cold nuclear matter.