In the distributed Raman optical fiber temperature measurement system, Anti-Stokes light and Stokes light have different propagation speeds due to the fiber dispersion effect, this will cause mismatch of the acquisition signals, resulting in measurement error. A method was proposed to use the piecewise cubic Hermite interpolation algorithm to correct the Anti-Stokes signal, eliminating signal mismatch and reducing the system measurement error. The method is verified on our 1 km sensing prototype. Before correction, the Anti-Stokes signals have one point more than the Stokes signals, causing -7.45% error at front of the temperature peak. After interpolation correction, the signal mismatch is eliminated, resulting in the system measurement error within ±1.5%.