We are developing insert devices for existing PET scanners to improve the image resolution with almost the same sensitivity as current PET scanners. The insert device can be used to zoom into a particular organ of interest. Introduction of the insert inside the scanner leads to three types of coincidences: insert-insert (II), insert-scanner (IS) and scanner-scanner (SS). In typical whole-body PET scanners, coincidences recorded in the scanner are sorted into parallel-beam sinograms and images are reconstructed using linear or iterative techniques. In the PET-insert system, the coincidences of type IS have an inherent fanbeam geometry. Reconstruction using parallel-beam sinograms introduces severe streaking artifacts in the images. The coincidences sorted into fan-beam sinograms reduce the artifacts in the reconstructed images. The approach to compute the kernel was derived from CT as there exists an analogy between the PET-insert geometry and a fourth generation CT scanner geometry. In this approach, the weights in the kernel are computed using the intersection of a cone with a voxel. We previously developed two dimensional reconstruction algorithms for this novel system geometry. We extend this work to three dimensions in this paper. A maximum-likelihood expectation-maximization algorithm was used to reconstruct the data. The kernel was validated with a contrast recovery study using a digital phantom. Images reconstructed from experimental data show good quality without any visible artifacts.