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We present a quantitative method for the nondestructive detection of concealed contraband based on terahertz transmission spectroscopy. Without knowing the prior information of barrier materials, the amount of concealed contraband can be extracted by approximating the terahertz absorbance spectrum of the barrier material with a low-order polynomial and then fitting the measured absorbance spectrum of the inspected object with the polynomial and the known standard spectrum of this kind of contraband. We verify the validity of this method using a sample of explosive 1,3,5-trinitro-s-triazine (RDX) covered with several different barrier materials which are commonly encountered in actual inspection, and good agreement between the calculated and actual value of the amount of RDX is obtained for the experiments performed under both nitrogen and air atmospheres. This indicates that the presented method can achieve quantitative detection of hidden contraband, which is important for security inspection applications.