The 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 waveguides. 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 supercontinuum generation to control spatiotemporal alignment for pump and signal pulses. The supercontinuum is directly coupled into a chirped periodically poled LiNbO3 waveguide for the 3–4 μm idler generation. A mid-infrared dual-comb spectrometer based on this approach provides a 100 MHz resolution over 25 THz coverage. To evaluate the applicability for spectroscopy, we measure the methane spectrum using the dual-comb spectrometer. 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.