In this paper, we present Calibration Recurrent Convolutional Neural Network (CalibRCNN) to infer a 6 degrees of freedom (DOF) rigid body transformation between 3D LiDAR and 2D camera. Different from the existing methods, our 3D-2D CalibRCNN not only uses the LSTM network to extract the temporal features between 3D point clouds and RGB images of consecutive frames, but also uses the geometric loss and photometric loss obtained by the interframe constraint to refine the calibration accuracy of the predicted transformation parameters. The CalibRCNN aims at inferring the correspondence between projected depth image and RGB image to learn the underlying geometry of 2D-3D calibration. Thus, the proposed calibration model achieves a good generalization ability to adapt to unknown initial calibration error ranges, and other 3D LiDAR and 2D camera pairs with different intrinsic parameters from the training dataset. Extensive experiments have demonstrated that our CalibRCNN can achieve state-of-the-art accuracy by comparison with other CNN based methods.