Laser heterodyne detection boasts exceptional advantages such as high spectral resolution and high signal-to-noise ratio (SNR). It excels at capturing spectral line broadening information of upper atmospheric molecules, which presents substantial research value in the realms of greenhouse gas profile measurement and the assessment of laser propagation effects in the atmosphere. This paper delves into the investigation of the processing method for heterodyne signals, adopting a non-modulated signal processing method to construct a near-infrared non-modulated laser heterodyne radiometer. This innovative design significantly enhanced the response speed and SNR. The radiometer achieved a spectral resolution of 0.006 cm-1 and an SNR of 300. This facilitated the acquisition of vertical profile distribution and column concentration of CH4 by measuring the absorption spectrum. Comparative tests revealed compelling advantages of the non-modulated device. The modulated device collected data 6 times in 6 minutes, yielding an SNR of 58. In contrast, the non-modulated device demonstrated superior efficiency by collecting data 6000 times in 2 minutes, resulting in a remarkable SNR of 103. In the process of inversion, the influence of the solar spectrum was coupled to improve the accuracy of inversion results. The inversion results of the CH4 column concentration from the laser heterodyne radiometer were compared with those from the Fourier transform spectrometer (EM27/SUN), with average concentrations of 1.946 ppmv and 1.930 ppmv, and exhibited an overall deviation of approximately 0.8%. The non-modulated laser heterodyne radiometer provides a new reference for the rapid, accurate and high spectral resolution measurements of greenhouse gas concentration.