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%.