Long memory reflects the continuing impact of random shock on its future values by depicting the dependence of observations far apart. Long memory in the dynamic of inflation decides monetary policy effect directly. Whether there is structural break in long memory is important to the design and implementation of monetary policy. This paper characterizes statistical nature of long memory in the dynamic of China inflation, Shimotsu's Wald statistics and Bai & Perrron's multiple structural break analysis are used to investigate the intrinsic structural instability of inflation long memory. Empirical results suggest that long memory in inflation dynamic is notable before 1996, after it declines significantly. This paper discusses the implications of the finding to relevant monetary policy analysis based on the impulse response function.