The third intracellular loop (ICL3) in the cytosolic face of glucagon receptor (GCGR) experiences significant conformational transition during receptor activation. It thus offers an attractive site for the introduction of organic fluorophores in our efforts to construct fluorescence-based GPCR biosensors. Herein, we report our confocal microscopic study of intracellular fluorescent labeling of ICL3 using a bioorthogonal chemistry strategy. Our approach involves the site-specific introduction of a strained alkene amino acid into the ICL3 through genetic code expansion, followed by a highly specific inverse electron-demand Diels-Alder reaction with the fluorescent tetrazine probes. Among the three strained alkene amino acids examined, both SphK and 2'-aTCOK offered successful fluorescent labeling of GCGR ICL3 with the appropriate tetrazine probes. At the same time, 4'-TCOK gave high background fluorescence due to its intracellular retention. The fluorescent tetrazine probes were designed following a computational model for background-free intracellular fluorescent labeling; however, their performance varied significantly in live-cell imaging as the strong non-specific signals interfered with the specific ones. Among all GCGR ICL3 mutants bearing a strained alkene, the H339SphK/2'-aTCOK mutants provided the best reaction partners for the BODIPY-Tz1/4 reagents in the bioorthogonal labeling reactions. The results from this study highlight the challenges in identifying bioorthogonal reactant pairs suitable for intracellular labeling of low-abundance receptors in live-cell imaging studies.