This paper uses terahertz (THz) spectroscopy for the first time as a simple method for estimating the molecular weight of a polymer across a very wide range. The viscosity average molecular weight (Mv) was measured and estimated as the molecular weight. Currently, to measure the Mv, a sample is dissolved in a solvent then measured its inherent viscosity. However, this procedure is complicated and time-consuming in practice. Additionally, as the molecular weight increases, the measurement accuracy decreases if Mv of a sample is above 3 million. Therefore, a new simple method is desired. A linear high-density polyethylene sample with an Mv range of 0.1 to 7.4 million was used. THz absorbance spectra of the samples were measured from 50 to 600 cm-1 (1.5 to 18 THz) then the multivariable analysis technique was applied. Consequently, a very high correlation coefficient (R2 ≈ 1) between the estimated and the measured Mv values were obtained across the range of the samples. This method is essential and suitable for industrial applications.