Single-cell transcriptomics is a powerful approach for characterizing gene transcription at cellular resolution. This approach requires efficient computational pipelines to undertake essential tasks, including clustering, dimensionality reduction, imputation, and denoising. Currently, most such pipelines undertake these computational tasks separately without considering the interdependence among these tasks. Here, we present an advanced pipeline, MUSIC-GCN, by employing a graph convolutional neural (GCN) network and autoencoder to perform multi-task single-cell RNA-sequencing (scRNA-seq) data analysis. The rationale is that multiple related tasks can be carried out simultaneously to enable enhanced learning and more effective representations through the ‘sharing of knowledge’ regarding individual tasks. Benchmarking experiments using various scRNA-seq datasets show that MUSIC-GCN can achieve a competitive performance on multi-tasks when benchmarked with state-of-the-art approaches.