Cell identity genes are distinct from other genes with respect to the epigenetic mechanisms to activate their transcription, e.g. by super-enhancers and broad H3K4me3 domains. However, it remains unclear whether their post-transcriptional regulation is also unique. We performed a systematic analysis of transcriptome-wide RNA stability in nine cell types and found that unstable transcripts were enriched in cell identity-related pathways while stable transcripts were enriched in housekeeping pathways. Joint analyses of RNA stability and chromatin state revealed significant enrichment of super-enhancers and broad H3K4me3 domains at the gene loci of unstable transcripts. Intriguingly, the RNA m6A methyltransferase, METTL3, preferentially binds to chromatin at super-enhancers, broad H3K4me3 domains and their associated genes. METTL3 binding intensity is positively correlated with RNA m6A methylation and negatively correlated with RNA stability of cell identity genes, probably due to co-transcriptional m6A modifications promoting RNA decay. Nanopore direct RNA-sequencing showed that METTL3 knockdown has a stronger effect on RNA m6A and mRNA stability for cell identity genes. Our data suggest a run-and-brake model, where cell identity genes undergo both frequent transcription and fast RNA decay to achieve precise regulation of RNA expression.