Electrohydrodynamic direct-writing (EHD-DW), a near-field electrospinning process, is considered as a promising technique to generate nanofibers in a non-contact, continuous, and controllable manner. However, the effect of process parameters on EHD-DW fibers' structures and the effect of fibers' structures on their properties have not yet been fully investigated. In this work, polycaprolactone (PCL) solution was used to fabricate EHD-DW fibers for investigating the process-structure-property correlations of EHD-DW. Three working modes of the electrospinning process and their corresponding regions in the process parameter space were studied. The surface roughness of EHD-DW fibers fabricated at different process parameters was measured. The impact of the surface roughness on the number and morphology of human mesenchymal stem cells (hMSCs) attached to the EHD-DW fibers was investigated. The results suggest that the surface roughness, which can be controlled by the process parameters of EHD-DW, can significantly affect the attachment of hMSCs. The cell density upon seeding can be largely improved by tuning the process parameters to achieve a favorable surface roughness. This work revealed the process-structure-property correlations of EHD-DW technology. Guidelines for controlling the morphology and cellular adhesion of EHD-DW fibers are provided based on the results of this study.