The mid-infrared dual-comb spectroscopy has innovated the detection of trace gases due to its high resolution, high sensitivity, and short response time. The traditional dual-comb system based on mode-locked lasers, electro-optic modulation or nonlinear optical micro-resonators is always combined with shortcomings of complex structure, high cost, few comb teeth, and poor practicability. In recent years, dual-wavelength mode-locked lasers that allow two asynchronous pulse trains to oscillate simultaneously have attracted increasing attention owing to their great potential in facilitating robust and precise dual-comb spectroscopy. In this paper, with two collimators and a segment of polarization-maintaining fiber acting as a Lyot filter, two asynchronous pulse trains centered at 1 034 nm and 1 039 nm respectively can emit from a single-cavity dual-wavelength laser, which is based on a Nonlinear Amplifying Loop Mirror structure. The repetition rate difference between the dual-wavelength pulses is about 1.18 kHz and the 3 dB spectral width per wavelength is ~1.6 nm. The mutual coherence is maintained owing to a shared laser cavity, and common-mode noise is canceled. The radio frequencies of the dual-wavelength pulses are traced and ~60 Hz frequency drift of each wavelength is measured within 10 hours yet only a 3.5 Hz frequency shift and 0.45 Hz standard deviation of the repetition rate difference is observed. The difference in magnitude indicates the high coherence and great environmental stability of the dual-wavelength pulses. To demonstrate the coherence between the dual-wavelength pulses, the multiheterodyne beat notes are detected. Because of the optical spectral overlap, the mode-resolved beat notes with a frequency interval of 1.18 kHz and ~25 dB signal-to-noise ratio are observed. Limited by the resolution bandwidth of the spectrum analyzer, the obtained full width at half maximum of each beat note is about 12 Hz. The average power of the seed pulses is scaled up to 1.1 W with a cascade amplifier to avoid excessive spontaneous emission noise and maintain high coherence. Then, the amplified pulses transform into a mid-infrared band by difference frequency generation with a 2 W continuous laser centered at 1 549.315 nm in the periodically polarized lithium niobite crystal. To improve the conversion efficiency, the temperature of the periodically polarized lithium niobite crystal is accurately controlled at 125 ℃ by high precision temperature control furnace. The power of the generated mid-infrared laser reaches 3.5 mW, and the corresponding spectrum covers more than 50 nm. The spectral width could be expanded by tuning the wavelength of the continuous laser. Moreover, the coherence of the mid-infrared dual-comb is measured and its frequency interval, signal-to-noise ratio and linewidth are consistent with the fundamental dual-comb. According to the Lambert-Beer theory, the absorption intensity of light is proportional to the concentration of the gas molecules and the length of the optical path. Hence, a multi-pass gas cell with an optical path of up to 10 m is employed. The generated mid-infrared laser experiences 50 times of reflection in the gas cell, which can greatly extend the interaction length and is conducive to the detection of trace gases. In a word, we have developed an integrated mid-infrared dual-comb system based on a single-cavity dual-wavelength laser. The two asynchronous pulse trains centered at 1 034 and 1 039 nm with a repetition rate difference of 1.18 kHz can replace the traditional complicated mode-locked lasers and show high coherence due to the suppression of the common-mode noise. The seed pulses are transformed into a mid-infrared band by difference frequency generation in the periodically polarized lithium niobite crystal. The generated mid-infrared dual-comb characteristics are consistent with the fundamental dual-comb. The integrated mid-infrared dual-comb system demonstrated in this paper can provide a potential approach for trace gases detection under complicated conditions.