Burns are a global public health problem, which brings great challenges to public health and the economy. Severe burns often lead to systemic infection, shock, multiple organ failure, and even death. With the increasing demand for the therapeutic effect of burn wounds, traditional dressings have been unable to meet people's needs due to their single function and many side effects. In this context, electrospinning shows a great prospect on the way to open up advanced wound dressings that promote wound repairing and prevent infection. With its large specific surface area, high porosity, and similar to natural extracellular matrix (ECM), electrospun nanofibers can load drugs and accelerate wound healing. It provides a promising solution for the treatment and management of burn wounds. This review article introduces the concept of burn and the types of electrospun nanofibers, then summarizes the polymers used in electrospun nanofiber dressings. Finally, the drugs (plant extracts, small molecule drugs and nanoparticles) loaded with electrospun burn dressings are summarized. Some promising aspects for developing commercial electrospun burn dressings are proposed.