This paper reports an efficient fabrication of N-doped graphene quantum dots (GQDs) showing controllable chemical and fluorescence (FL) properties through infrared carbonization (IRC) of citric acid and urea. The GQDs prefer to form an equilibrium shapes of circle with an average particle size ranged from 5 to 10 nm. The N/C atomic ratio in GQDs can be precisely tailored in a range from 21.6 to 49.6 at.% by simply controlling the weight ratio of citric acid to urea. With increasing the urea content, the GQDs not only contain N-doped graphene but also incorporate with crystalline cyanuric acid, forming a binary crystallinity. The quantum yield of 22.2% is achieved by N-doped GQDs, prepared from the IRC synthesis of chemical precursor at the citric acid/urea at 3:1. Excessive N and cyanuric acid can lead to FL quenching, red shift and wide spectral distribution. The design of GQDs possesses a multiple chromophoric band-gap structure, originated from the presence of cyanuric acid, defect-related emissive traps, and functional group distributions. This work offers an effective and inspiring approach to engineering both chemical compositions and unique crystalline structures of GQDs, and will therefore facilitate their fundamental research and applications to optical, sensing, energy and biological fields.