Mid-infrared optical frequency comb is a powerful tool for gas sensing. In this study, we demonstrate a simple mid-infrared dual-comb spectrometer covering 3–4 μm in LiNbO3 waveguide. Based on a low-power fiber laser system, the mid-infrared comb is achieved via intra-pulse difference frequency generation in the LiNbO3 waveguide. We construct pre-chirp management before a highly nonlinear fiber to optimize the supercontinuum generation. The supercontinuum is coupled into a LiNbO3 waveguide for the 3–4 μm idler generation. Based on this method, we built two combs to realize a dual-comb spectrometer with a 100 MHz resolution over 25 THz spectral coverage. To evaluate the applicability of spectroscopy, we measure the methane spectrum. The measured results are consistent with the HITRAN database, in which the root mean square of the residual is 3.2%. This proposed method is expected to develop integrated and robust mid-infrared dual-comb spectrometers on chip for sensing.