Wavefront coding (WFC) techniques, including optical coding and digital image processing stages, enable significant capabilities for extending the depth of field of imaging systems. In this study, we demonstrated a deeply learned far-infrared WFC camera with an extended depth of field. We designed and optimized a high-order polynomial phase mask by a genetic algorithm, exhibiting a higher defocus consistency of the modulated transfer functions than works published previously. Additionally, we trained a generative adversarial network based on a synthesized WFC dataset for the digital processing part, which is more effective and robust than conventional decoding methods. Furthermore, we captured real-world infrared images using the WFC camera with far, middle, and near object distances. Their results after wavefront coding/decoding showed that the model of deeply learned networks improves the image quality and signal-to-noise ratio significantly and quickly. Therefore, we construct a novel artificial intelligent method of deeply learned WFC optical imaging by applying infrared wavelengths, but not limited to, and provide good potential for its practical application in "smart" imaging and large range target detection.