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Abstract Single cell profiling techniques including multi-omics and spatial-omics technologies allow researchers to study cell-cell variation within a cell population. These variations extend to biological networks within cells, in particular, the gene regulatory networks (GRNs). GRNs rewire as the cells evolve, and different cells can have different governing GRNs. However, existing GRN inference methods usually infer a single GRN for a population of cells, without exploring the cell-cell variation in terms of their regulatory mechanisms. Recently, jointly profiled single cell transcriptomics and chromatin accessibility data have been used to infer GRNs. Although methods based on such multi-omics data were shown to improve over the accuracy of methods using only single cell RNA-seq (scRNA-seq) data, they do not take full advantage of the single cell resolution chromatin accessibility data. We propose CeSpGRN (CellSpecificGeneRegulatoryNetwork inference), which infers cell-specific GRNs from scRNA-seq, single cell multi-omics, or single cell spatial-omics data. CeSpGRN uses a Gaussian weighted kernel that allows the GRN of a given cell to be learned from the sequencing profile of itself and its neighboring cells in the developmental process. The kernel is constructed from the similarity of gene expressions or spatial locations between cells. When the chromatin accessibility data is available, CeSpGRN constructs cell-specific prior networks which are used to further improve the inference accuracy. We applied CeSpGRN to various types of real-world datasets and inferred various regulation changes that were shown to be important in cell development. We also quantitatively measured the performance of CeSpGRN on simulated datasets and compared with baseline methods. The results show that CeSpGRN has a superior performance in reconstructing the GRN for each cell, as well as in detecting the regulatory interactions that differ between cells. CeSpGRN is available athttps://github.com/PeterZZQ/CeSpGRN.