Atmospheric greenhouse gases have great influence on the climate forcing, which is important to human being and also for natural systems. Nitrous oxide (N2O), such as carbon dioxide and methane, is an important greenhouse gas. It plays an important role in the atmospheric environment. Therefore, sensitive measurement of N2O concentration is of significance for studying the atmospheric environment. In this paper, a photoacoustic spectroscopy (PAS) system based on 7.6 m mid infrared quantum cascade laser combined with resonant PAS technique is established for the sensitive detection of N2O concentration. The PAS has been regarded as a highly sensitive and selective technique to measure trace gases. Compared with laser absorption spectroscopy, the PAS offers several intrinsic attractive features including ultra-compact size and no cross-response of light scattering. In addition, the signal of PAS is recorded with low-cost wavelength-independent acoustic transducer. The performance of the developed system is optimized and improved based on the traditional photoacoustic spectroscopic detection. Dual beam enhancement method is used to increase the effective optical power which effectively improves the detection sensitivity of the system. The N2O absorption line at 1307.66 cm-1 is chosen as the target line, and an operation pressure of 50 kPa is selected for reducing cross-talking from H2O absorption line. By detecting the photoacoustic signals of a certain concentration of N2O at different modulation frequencies and modulation amplitudes, the optimal modulation frequency and modulation amplitude of the system are determined to be 800 Hz and 90 mV, respectively. Different concentrations of N2O gas are detected under the optimized parameters, and calibration curve of the system, that is, the curve of photoacoustic signal versus concentration of N2O is obtained, which shows good linearity. The experimental results show that the minimum detection limit of the system is 150 ppb at a pressure of 50 kPa with an integration time of 30 ms. The system noise can be further reduced by increasing the averaging time. A minimum detection limit of 37 ppb is achieved by averaging signals 100 times, and the signal of N2O in the atmosphere is obtained.