We calculate the cross-correlation function (CCF) between damped Ly-a systems (DLAs) and Lyman break galaxies (LBGs) using cosmological hydrodynamic simulations at z=3. We compute the CCF with two different methods. First, we assume that there is one DLA in each dark matter halo if its DLA cross section is non-zero. In our second approach we weight the pair-count by the DLA cross section of each halo, yielding a cross-section-weighted CCF. We also compute the angular CCF for direct comparison with observations. Finally, we calculate the auto-correlation functions of LBGs and DLAs, and their bias against the dark matter distribution. For these different approaches, we consistently find that there is good agreement between our simulations and observational measurements by Cooke et al. and Adelberger et al. Our results thus confirm that the spatial distribution of LBGs and DLAs can be well described within the framework of the concordance Lambda CDM model. We find that the correlation strengths of LBGs and DLAs are consistent with the actual observations, and in the case of LBGs it is higher than would be predicted by low-mass galaxy merger models.