Sugars play important roles in many aspects of plant growth and development, acting as both energy sources and signaling molecules. With the successful use of genetic approaches, the molecular components involved in sugar signaling have been identified and their regulatory roles in the pathways have been elucidated. Here, we describe novel mutants of Arabidopsis (Arabidopsis thaliana), named glucose insensitive growth (gig), identified by their insensitivity to high-glucose (Glc)-induced growth inhibition. The gig mutant displayed retarded growth under normal growth conditions and also showed alterations in the expression of Glc-responsive genes under high-Glc conditions. Our molecular identification reveals that GIG encodes the plastidial copper (Cu) transporter PAA1 (for P(1B)-type ATPase 1). Interestingly, double mutant analysis indicated that in high Glc, gig is epistatic to both hexokinase1 (hxk1) and aba insensitive4 (abi4), major regulators in sugar and retrograde signaling. Under high-Glc conditions, the addition of Cu had no effect on the recovery of gig/paa1 to the wild type, whereas exogenous Cu feeding could suppress its phenotype under normal growth conditions. The expression of GIG/PAA1 was also altered by mutations in the nuclear factors HXK1, ABI3, and ABI4 in high Glc. Furthermore, a transient expression assay revealed the interaction between ABI4 and the GIG/PAA1 promoter, suggesting that ABI4 actively regulates the transcription of GIG/PAA1, likely binding to the CCAC/ACGT core element of the GIG/PAA1 promoter. Our findings indicate that the plastidial Cu transporter PAA1, which is essential for plastid function and/or activity, plays an important role in bidirectional communication between the plastid and the nucleus in high Glc.