The greenhouse effect has a great impact on the earth's environment and climate, so accurate detection of greenhouse gases is of great significance. As one of the important greenhouse gases, nitrous oxide (N₂O) has a much higher greenhouse effect potential than carbon dioxide (CO₂). However, compared to the widely studied CO₂ and methane (CH₄), there is less research on N₂O. In this paper, a system based on a domestically developed 7.6 μm mid infrared quantum cascade laser was established for atmospheric N₂O detection. The system adopts wavelength modulation and the second harmonic detection technology, with the N₂O absorption line at 1307.66 cm^-1 as the target line. Firstly, the optimal modulation amplitude of the system was determined by detecting the second harmonic signal of a certain concentration of N₂O at different modulation amplitudes. Then under the optimal experimental conditions, N₂O gas with different concentrations was measured, and the signal-volume fraction calibration curve of the system was obtained. The results showed that the minimum detection limit of N₂O volume fraction of the system was 1.34 × 10^-9, indicating that the system can meet the needs of atmospheric N₂O measurement. A 6-hour detection of N₂O was further carried out, and the averaged volume fraction of N₂O during detection was 325 × 10^-9, which is equivalent to the well-known volume fraction of atmospheric N₂O of 320 × 10^-9.