An infrared temperature-measurement method based on a radial basis function (RBF) neural network is established in the case of unknown target emissivity. First, the strong nonlinear relationship between the target temperature and the peak of the radiance curve and its wavelength is derived. The inputs to the neural network are determined. Then, according to the RBF network, sample data are studied, and a target radiation-temperature-measurement model is established. The model does not require emissivity. A blackbody and steel plate target are used as test targets to prove the proposed method. The maximum relative error of the temperature of the blackbody is 0.016% and that of the steel plate is 1.08%. These results verify the rationality of the established temperature-measurement method.