The sensors based on intracavity intensity modulation of fiber ring laser (FRL) have shown excellent performance in sensing resolution and detection limit, but suffer from large measurement errors. The measurement errors mainly result from the power fluctuation of pump source and environmental interference. Therefore, the methods of error suppression are of great significance for FRL sensors. In this paper, a temperature measurement method with error suppression is performed by a dual-wavelength FRL with an intracavity Sagnac interferometer. The sensing principle of single- and dual-wavelength FRL sensors have been analyzed. By the sensing manner of intensity difference of two excited wavelengths, the measurement error has been decreased from 0.443% to 0.066% compared with the single-wavelength configuration. The temperature sensitivity and measurement stability have been further discussed. This method can be extended to similar FRL sensors to suppress measurement errors.