The electrospinning technique is being widely explored in the biomedical field due to its simplicity to produce meshes and its capacity to mimic the micro-nanostructure of the natural extracellular matrix. For skin tissue engineering applications, wound dressings made from electrospun nanofibers present several advantages compared to conventional dressings, such as the promotion of the hemostasis phase, wound exudate absorption, semi-permeability, easy conformability to the wound, functional ability and no scar induction. Despite being a relatively simple technique, electrospinning is strongly influenced by polymer solution characteristics, processing parameters and environmental conditions, which strongly determine the production of fibers and their morphology. However, most electrospinning systems are wrongly designed, presenting a large number of conductive components that compromises the stability of the spinning process. This paper presents a new design of an electrospinning system solving the abovementioned limitations. The system was assessed through the production of polycaprolactone (PCL) and gelatin nanofibers. Different solvents and processing parameters were considered. Results show that the proposed electrospinning system is suitable to produce reproducible and homogeneous electrospun fibers for tissue engineering applications.