Accurate determination of dose-rate constant (lambda) for interstitial brachytherapy sources emitting low-energy photons (< 50 keV) has remained a challenge in radiation dosimetry because of the lack of a suitable absolute dosimeter for accurate measurement of the dose rates near these sources. Indeed, a consensus value of lambda taken as the arithmetic mean of the dose-rate constants determined by different research groups and dosimetry techniques has to be used at present for each source model in order to minimize the uncertainties associated with individual determinations of lambda. Because the dosimetric properties of a source are fundamentally determined by the characteristics of the photons emitted by the source, a new technique based on photon spectrometry was developed in this work for the determination of dose-rate constant. The photon spectrometry technique utilized a high-resolution gamma-ray spectrometer to measure source-specific photon characteristics emitted by the low-energy sources and determine their dose-rate constants based on the measured photon-energy spectra and known dose-deposition properties of mono-energetic photons in water. This technique eliminates many of the difficulties arising from detector size, the energy dependence of detector sensitivity, and the use of non-water-equivalent solid phantoms in absolute dose rate measurements. It also circumvents the uncertainties that might be associated with the source modeling in Monte Carlo simulation techniques. It was shown that the estimated overall uncertainty of the photon spectrometry technique was less than 4%, which is significantly smaller than the reported 8-10% uncertainty associated with the current thermo-luminescent dosimetry technique. In addition, the photon spectrometry technique was found to be stable and quick in lambda determination after initial setup and calibration. A dose-rate constant can be determined in less than two hours for each source. These features make it ideal to determine the dose-rate constant of each source model from a larger and more representative sample of actual sources and to use it as a quality assurance resource for periodic monitoring of the constancy of lambda for brachytherapy sources used in patient treatments.