Three-dimensional(3D) flame chemiluminescence tomography (FCT) is realized in multi-direction and multi-angle using traditional iterative algorithms. However, 3D-FCT is often challenged by insufficient sampling data because of the limited observation windows provided in practical for flame measurement. To obtain flame multiple projections in limited observation windows, we develop a camera array arrangement in FCT. In addition, a residual network with a new loss function combing physical model of flame is proposed to achieve higher reconstruction accuracy, faster reconstruction speed and efficient image feature in residual network for 3D FCT measurement. Furthermore, the determination of the weight coefficient in the loss function is performed by numerical simulation experiments. The flame reconstruction results show that the proposed residual network method including the new loss function has more reliable structural similarity and noise immunity compared with the ART algorithm and the CNN algorithm. This work provides a faster and more accurate method for combustion diagnosis under limited observation windows with insufficient projections.