The apricot (Prunus armeniaca L.) is a fruit that belongs to the Rosaceae family; it has a unique flavor and is of important economic and nutritional value. The composition and content of soluble sugars and organic acids in fruit are key factors in determining the flavor quality. However, the molecular mechanism of sugar and acid accumulation in apricots remains unclear. We measured sucrose, fructose, glucose, sorbitol, starch, malate, citric acid, titratable acid, and pH, and investigated the transcriptome profiles of three apricots (the high-sugar cultivar ‘Shushanggan’, common-sugar cultivar ‘Sungold’, and low-sugar cultivar ‘F43’) at three distinct developmental phases. The findings indicated that ‘Shushanggan’ accumulates a greater amount of sucrose, glucose, fructose, and sorbitol, and less citric acid and titratable acid, resulting in a better flavor; ‘Sungold’ mainly accumulates more sucrose and less citric acid and starch for the second flavor; and ‘F43’ mainly accumulates more titratable acid, citric acid, and starch for a lesser degree of sweetness. We investigated the DEGs associated with the starch and sucrose metabolism pathways, citrate cycle pathway, glycolysis pathway, and a handful of sugar transporter proteins, which were considered to be important regulators of sugar and acid accumulation. Additionally, an analysis of the co-expression network of weighted genes unveiled a robust correlation between the brown module and sucrose, glucose, and fructose, with VIP being identified as a hub gene that interacted with four sugar transporter proteins (SLC35B3, SLC32A, SLC2A8, and SLC2A13), as well as three structural genes for sugar and acid metabolism (MUR3, E3.2.1.67, and CSLD). Furthermore, we found some lncRNAs and miRNAs that regulate these genes. Our findings provide clues to the functional genes related to sugar metabolism, and lay the foundation for the selection and cultivation of high-sugar apricots in the future.