Single cell gene expression datasets have been used to uncover differences between single cells, leading to discoveries of new cell types and cell identities, which are usually defined by the transcriptome profiles of cells. Biological networks, in particular, gene regulatory networks (GRNs), can be viewed as another feature of the cells, that contributes to the uniqueness of each single cell. However, methods that reconstruct cell-specific GRNs are still missing. We propose CeSpGRN (Cell Specific GRN), which infers cell-specific GRNs from single cell gene expression data. CeSpGRN uses a Gaussian weighted kernel which allows the GRN of a given cell to be learned from the gene expression profile of this cell and cells that are upstream and downstream of this cell in the developmental process. CeSpGRN can be applied to infer cell-specific GRNs in cell populations of any trajectory or cluster structure, and it does not require time information of cells as additional input. We compared the performance of CeSpGRN and baseline methods on simulated datasets obtained under various settings. CeSpGRN showed superior performance in reconstructing the GRN for each cell, as well as in detecting the regulatory interactions that differ between cells. We also applied CeSpGRN to real datasets including THP-1 human myeloid monocytic leukemia cells and mouse embryonic stem cells, where CeSpGRN suggested a set of interactions between genes that rewire during the differentiation process in these cells.