Multi-spectral radiation temperature measurement measures multiple spectral radiation intensity information of a certain point of the object to be measured and obtain the true temperature through the Planck formula inversion. However, the unknown spectral emissivity is the biggest obstacle to the inversion process of multi-spectral radiation temperature measurement. At present, a set of emissivity models (emissivity-wavelength or emissivity-temperature models) are often used in advance. If the assumption model matches the actual situation, the inversion result can meet the requirements. If the assumption model does not match the actual situation, the reverse result of the performance is a very error. Whether it can realize the direct inversion of true temperature and spectral emissivity without any hypothetical model of spectral emissivity has always been a hot and difficult point in the theoretical research of multi-spectral radiation temperature measurement. For this reason, a generalized inverse matrix-coordinate rotation algorithm is proposed to transform the inversion problem of multi-spectral radiation temperature measurement into a constrained optimization problem. Since the generalized inverse method needs to constrain the emissivity range, and the coordinate rotation method needs to set a proper initial emissivity value, considering the respective advantages and disadvantages of the two algorithms, the two algorithms can be combined. The minimum norm solution obtained by the generalized inverse method is used as the initial point of the iterative search in the constrained optimization algorithm, which further improves the adaptability of the algorithm to the emissivity of different materials. In order to verify whether the algorithm can find a special solution that meets the thermophysical parameters (emissivity) and true temperature of the target under test without considering the assumed relationship between emissivity and wavelength, six types of targets with a representative emissivity change trend are selected Material is simulated experiment. The simulation results of six different spectral emissivity models show that the new algorithm does not require any prior knowledge about emissivity, and the inversion results of different emissivity models perform well. In the case of a true temperature of 1 800 K, the absolute error and relative errors are less than 5.0%. Compared with the gradient projection method, the calculation efficiency is increased by 202 times on average. It shows that the algorithm has the advantages of not considering any prior knowledge of spectral emission rate, fast inversion speed and being suitable for various emission models. It further improves the theory of multi-spectral radiation temperature measurement and has good application prospects in high-temperature measurement.