Forest-type classification is a very complex and difficult subject. The complexity increases with urban and peri-urban forests because of the variety of features that exist in remote sensing images. The success of forest management that includes forest preservation depends strongly on the accuracy of forest-type classification. Several classification methods are used to map urban and peri-urban forests and to identify healthy and non-healthy ones. Some of these methods have shown success in the classification of forests where others failed. The successful methods used specific remote sensing data technology, such as hyper-spectral and very high spatial resolution (VHR) images. However, both VHR and hyper-spectral sensors are very expensive, and hyper-spectral sensors are not widely available on satellite platforms, unlike multi-spectral sensors. Moreover, aerial images are limited in use, very expensive, and hard to arrange and manage. To solve the aforementioned problems, an advanced method, self-organizing–deep learning (SO-UNet), was created to classify forests in the urban and peri-urban environment using multi-spectral, multi-temporal, and medium spatial resolution Sentinel-2 images. SO-UNet is a combination of two different machine learning technologies: artificial neural network unsupervised self-organizing maps and deep learning UNet. Many experiments have been conducted, and the results showed that SO-UNet overwhelms UNet significantly. The experiments encompassed different settings for the parameters that control the algorithms.