The extracellular matrix of bacterial biofilms consists of diverse components including polysaccharides, proteins and DNA. Extracellular RNA (eRNA) can also be present, contributing to the structural integrity of biofilms. However, technical difficulties related to the low stability of RNA make it difficult to understand the precise roles of eRNA in biofilms. Here, we show that eRNA associates with extracellular DNA (eDNA) to form matrix fibres in Pseudomonas aeruginosa biofilms, and the eRNA is enriched in certain bacterial RNA transcripts. Degradation of eRNA associated with eDNA led to a loss of eDNA fibres and biofilm viscoelasticity. Compared with planktonic and biofilm cells, the biofilm matrix was enriched in specific mRNA transcripts, including lasB (encoding elastase). The mRNA transcripts colocalised with eDNA fibres in the biofilm matrix, as shown by single molecule inexpensive FISH microscopy (smiFISH). The lasB mRNA was also observed in eDNA fibres in a clinical sputum sample positive for P. aeruginosa. Thus, our results indicate that the interaction of specific mRNAs with eDNA facilitates the formation of viscoelastic networks in the matrix of Pseudomonas aeruginosa biofilms.