Barkhausen noise (BN) is electromagnetic pulse sequence that could be used to nondestructively predict the properties of materials such as hardness, residual stress and carbon content. Current BN signal analysis methods fail to describe the highly variated BN signal and achieve high regression accuracy due to the low interpretability of neural network and limited capacity of mathematical regression tools. In this paper, two multi-variable regression tools, named partial Chebyshev polynomial regression (PCPR) and Mutual Information-based Feature Selection with Class-dependent Redundancy and multi-variable Chebyshev polynomials regression (MIFS-CR+MCPR), are employed for the first time to predict the hardness of Cr12MoV steel (i.e. X12m). Combined with Chebyshev polynomials, our regression tools are designed on the basis of cascaded regression and mutual-information-based feature selection. As represented by the experimental results for predicting the hardness of X12m, the proposed method outperforms other comparative methods including neural network and partial linear square regression method.