The classification of wound severity is a critical step in wound diagnosis. An effective classifier can help wound professionals categorize wound conditions more quickly and affordably, allowing them to choose the best treatment option. This study used wound photos to construct a deep neural network-based wound severity classifier that classified them into one of three classes: green, yellow, or red. The green class denotes wounds still in the early stages of healing and are most likely to recover with adequate care. Wounds in the yellow category require more attention and treatment than those in the green category. Finally, the red class denotes the most severe wounds that require prompt attention and treatment. A dataset containing different types of wound images is designed with the help of wound specialists. Nine deep learning models are used with applying the concept of transfer learning. Several stacked models are also developed by concatenating these transfer learning models. The maximum accuracy achieved on multi-class classification is 68.49%. In addition, we achieved 78.79%, 81.40%, and 77.57% accuracies on green vs. yellow, green vs. red, and yellow vs. red classifications for binary classifications.