The spectral reflectance of an object completely determines its surface color; therefore, studying the spectral reflectance is of great significance for industries with high requirements for color information. Direct acquisition of spectral reflectance requires precise and expensive equipment. However, the cost of obtaining spectral reflectance can be greatly reduced by establishing a model that predicts spectral reflectance from RGB response values obtained from low-cost devices such as digital cameras. Spectral reflectance reconstruction algorithms based on regression methods have received widespread attention, and their core goal is to establish a mapping relationship between RGB vectors and spectral reflectance vectors. For most objects, the spectral reflectance curves of their surfaces have the property of smoothing. Therefore, there is a certain correlation between the spectral reflectance components. However, the existing algorithms have built prediction models for each dimension of the spectral reflectance vector separately, without taking advantage of the correlation between the spectral reflectance components. Unlike traditional single-output regression methods, the multi-target stacking regression method utilizes the correlation between outputs by reinjecting the first predicted output values into the inputs, and this paper studies spectral reflectance reconstruction based on multi-target stacking regression. However, the traditional multi-target stacking regression method is susceptible to the influence of errors in the first predicted output values. To address this problem, this paper proposes a screening method for the first predicted output value, selecting the part with less error as input to ensure the accuracy of the next model-building step. This screening method can preserve the samples with lower errors to a great extent, even without knowing the true values. The experimental data set in this paper is sourced from the ICVL hyperspectral image database, and the evaluation metrics are root mean square error and chromaticity error. The experimental results indicate that the proposed multi-target screening stacking regression can overcome the problems of multi-target stacking regression and achieve smaller errors than without stacking. Therefore, the proposed method in this paper can better utilize the correlation between spectral reflectance components.