The Boltzmann constant can be optically determined by measuring the Doppler width of an absorption line of molecules at gas phase. We propose to apply a near infrared cavity ring-down (CRD) spectrometer for this purpose. The superior sensitivity of CRD spectroscopy and the good performance of the near-ir lasers can provide ppm (part-per-million) accuracy which will be competitive to present most accurate result obtained from the speed of sound in argon measurement. The possible influence to the uncertainty of the determined Doppler width from different causes are investigated, which includes the signal-to-noise level, laser frequency stability, detecting nonlinearity, and pressure broadening effect. The analysis shows that the CRD spectroscopy has some remarkable advantages over the direct absorption method proposed before. The design of the experimental setup is presented and the measurement of C2H2 line near 0.8 μm at room temperature has been carried out as a test of the instrument.