The crack propagation due to a thermal stress induced by a moving heat alog sine-curve is examined numerically and experimentally. The simulated crack path and crack propagation behavior accords well with observation. The ratio of wave amplitude a and wave length Λ of heat locus controles the behavior of crack growth. When a/Λ<0.2, the crack propagates stably. While a/Λ becomes large value, the apparent instablity of growth behavior including acceleration and deceleration of crack propagation can be found both in the simulation and the observation,