Phosphorene with tunable band gap and excellent electronic properties is a two dimensional semiconductor that have been demonstrated to be useful in many applications such as gas-sensing, photo-thermal and optoelectronic devices, battery and transistors. In this paper, we first investigate the electronic properties of phosphorene quantum dots, and then, parameters like the band gap, polar and IR spectra are investigated by doping structure with nitrogen atoms. For this progress, the density function theory has been used. It observed that the structures have a semiconductor band gap and this parameter decreases with increase the nitrogen atoms number and nitrogen doped. In addition, in the IR spectrum, with the increase in the number of nitrogen, a spatial displacement occurs towards lower frequencies due to fluctuations of nitrogen-phosphorus bonds. Therefore, phosphorene quantum dots can be used as a sensor for nitrogen-containing pollutants.