MOTIVATION: Understanding cell differentiation and development dynamics is key for single-cell transcriptome analysis. Current cell differentiation trajectory inference algorithms face challenges such as high dimensionality, noise, and a need for users to possess certain biological information about the datasets to effectively utilize the algorithms. Here, we introduce Trajectory Inference with Cell-Cell Interaction (TICCI), a novel way to address these challenges by integrating intercellular communication information. In recognizing crucial intercellular communication during development, TICCI proposes Cell-Cell Interactions (CCI) at single-cell resolution. We posit that cells exhibiting higher gene expression similarity patterns are more likely to exchange information via biomolecular mediators. RESULTS: TICCI is initiated by constructing a cell-neighborhood matrix using edge weights composed of intercellular similarity and CCI information. Louvain partitioning identifies trajectory branches, attenuating noise, while single-cell entropy (scEntropy) is used to assess differentiation status. The Chu-Liu algorithm constructs a directed least-square model to identify trajectory branches, and an improved diffusion fitted time algorithm computes cell-fitted time in nonconnected topologies. TICCI validation on single-cell RNA sequencing (scRNA-seq) datasets confirms the accuracy of cell trajectories, aligning with genealogical branching and gene markers. Verification using extrinsic information labels demonstrates CCI information utility in enhancing accurate trajectory inference. A comparative analysis establishes TICCI proficiency in accurate temporal ordering. AVAILABILITY AND IMPLEMENTATION: Source code and binaries freely available for download at https://github.com/mine41/TICCI, implemented in R (version 4.32) and Python (version 3.7.16) and supported on MS Windows. Authors ensure that the software is available for a full two years following publication.