The effect of notch volume on the mechanical behavior of a novel high-strength and high-toughness steel with negative Poisson's ratio effect (called NPR steel) was studied. First, the quasi-static tensile test of NPR steel with different notch volumes was carried out, and its failure characteristics and mechanical properties parameters were studied. Then, the modified Johnson-Cook (J-C) constitutive model with coupled notch volume ratio was proposed. The model was validated based on three-dimensional finite element numerical simulations. The results show that the engineering stress-strain curve of NPR steel has no yield platform, and has the mechanical properties of high strength, high elongation, and high energy absorption. Notch volume significantly affects the mechanical properties of NPR steel. The elongation, yield strength, tensile strength, and energy absorption characteristics of steel bar gradually decrease with the increase in notch volume. The notch volume ratio V*, a characteristic parameter describing the notch volume of reinforcement, is defined, and the quantitative relationship between this parameter and mechanical parameters is established, which can accurately characterize the mechanical properties of specimens with different notch volume ratios. Based on the true stress-strain curves with different notch volume ratios, a constitutive model with modified Johnson-Cook model parameters is proposed. The finite element results show that the modified J-C model can accurately fit the quasi-static tensile mechanical behavior of NPR steel.