The surface spectral reflectance of the object is regarded as the fingerprint of its color, and at the same time, it is also an important feature to characterize the physical and chemical properties of substances. Multispectral imaging technology that is based on spectral reconstruction can overcome the dependence of RGB images on imaging conditions. Meanwhile, it can effectively improve the spatial resolution and acquisition efficiency of multispectral images and reduce equipment costs. Different from the principle of multispectral cameras, multispectral imaging based on spectral reconstruction first capture the digital images of the object using a digital imaging system, and then the corresponding multispectral images are reconstructed using spectral reconstruction methods. However, due to the mechanism of current spectral reconstruction methods, for both machine learning and deep learning methods, they are sensitive to exposure change of the image in practice. This means the spectral reconstruction model established at one exposure level cannot be directly used at another exposure level, or the curve shape of the reconstructed spectral reflectance will deviate from the ground truth. The sensitivity to exposure changes of current spectral reconstruction methods has limited their application in open environments with variable illumination intensity and inhomogeneity. To deal with the problems of current methods, an adaptive weighted spectral reconstruction method based on polynomial root expansion is proposed in this paper. In the proposed method, the raw RGB response of samples is firstly expanded by the root polynomial, and then the spectral reconstruction model is established by the pseudo-inverse algorithm. It will ensure the proposed method will be against the exposure changes. After that, an adaptive weighting matrix is constructed in the spectral invariant feature space to improve the spectral reconstruction accuracy further. The proposed method is verified and compared with the existing method through theoretical experiments and three sample sets. Results show that the existing spectral reconstruction methods are all sensitive to exposure change, and the proposed method can effectively adapt to the exposure change. The spectral root-mean-square error (RMSE) and the color difference (ΔE*ab) are significantly lower than existing methods. In addition, results indicate that constructing the adaptive weighting matrix in spectrally invariant feature space is crucial to improve the spectral reconstruction accuracy of the proposed method. The research results are important for high-precision multispectral image acquisition in the open environment.