G protein-biased μ opioid receptor agonists have the potential to induce less receptor desensitisation and tolerance than balanced opioids. Here, we investigated if the cyclic endomorphin analogue Tyr-c[D-Lys-Phe-Tyr-Gly] (Compound 1) is a G protein-biased μ agonist and characterised its ability to induce rapid receptor desensitisation in mammalian neurones. The signalling and trafficking properties of opioids were characterised using bioluminescence resonance energy transfer assays, enzyme-linked immunosorbent assay and phosphosite-specific immunoblotting in human embryonic kidney 293 cells. Desensitisation of opioid-induced currents were studied in rat locus coeruleus neurones using whole-cell patch-clamp electrophysiology. The mechanism of Compound 1-induced μ receptor desensitisation was probed using kinase inhibitors. Compound 1 has similar intrinsic activity for G protein signalling as morphine. As predicted for a G protein-biased μ agonist, Compound 1 induced minimal agonist-induced internalisation and phosphorylation at intracellular μ receptor serine/threonine residues known to be involved in G protein-coupled receptor kinase (GRK)-mediated desensitisation. However, Compound 1 induced robust rapid μ receptor desensitisation in locus coeruleus neurons, to a greater degree than morphine. The extent of Compound 1-induced desensitisation was unaffected by activation or inhibition of protein kinase C (PKC) but was significantly reduced by inhibition of GRK. Compound 1 is a novel G protein-biased μ agonist that induces substantial rapid receptor desensitisation in mammalian neurons. Surprisingly, Compound 1-induced desensitisation was demonstrated to be GRK dependent despite its G protein bias. Our findings refute the assumption that G protein-biased agonists will evade receptor desensitisation and tolerance. This article is part of a themed issue on Advances in Opioid Pharmacology at the Time of the Opioid Epidemic. To view the other articles in this section visit http://onlinelibrary.wiley.com/doi/10.1111/bph.v180.7/issuetoc.