We report a Fabry-Perot interferometer (FPI)-based multi-channel micro-spectrometer used for multi-gas measurement in the spectral range of $3-5{mu}m$ and its gas sensing performance. The fabricated infrared (IR) spectrometer consists of two parts: an FPI on the top side for selective IR filtering and a $V_2O_5$-based IR detector array on the bottom side for the detection of the filtered IR. Experimental results show that the FPI-based multi-channel gas sensor has reliability and selectivity for simultaneously detecting environmentally harmful gases such as $CH_4$, $CO_2$, $N_2O$ and CO in the spectral range of $3-5{mu}m$. The fabricated FPI-based multi-channel gas sensor also demonstrated that a reliable and selective detection of gas concentrations ranging from 0 to 500 ppm is feasible. In addition, the electrical characteristics demonstrate a superior response performance in regards to the selectivity in the multi-target gases.