The reconstruction of 3D object from a single image is an important task in the field of computer vision. In recent years, 3D reconstruction of single image using deep learning technology has achieved remarkable results. Traditional methods to reconstruct 3D object from a single image require prior knowledge and assumptions, and the reconstruction object is limited to a certain category or it is difficult to accomplish a good reconstruction from a real image. Although deep learning can solve these problems well with its own powerful learning ability, it also faces many problems. In this paper, we first discuss the challenges faced by applying the deep learning method to reconstruct 3D objects from a single image. Second, we comprehensively review encoders, decoders and training details used in 3D reconstruction of a single image. Then, the common datasets and evaluation metrics of single image 3D object reconstruction in recent years are introduced. In order to analyze the advantages and disadvantages of different 3D reconstruction methods, a series of experiments are used for comparison. In addition, we simply give some related application examples involving 3D reconstruction of a single image. Finally, we summarize this paper and discuss the future directions.