Fatigue crack growth under thermal fluctuation is theoretically investigated by the use of a Markov approximation method, under the condition that the temporary variation of the inner surface temperature of the plate can be modeled as a narrow-band stationary process. First, under an assumption that the peak stress causes the crack growth, a crack growth equation is formulated based upon the Paris' law and it is extended to a random differential equation, in which the random variation of crack propagation resistances are also taken into account. Next, a residual life distribution as well as a probability distribution function of the crack growth processes is derived. Finally, some numerical examples are shown to examine the quantitative behavior of the residual life distribution in the highreliability region. The result indicates that the residual life in such a region is of order of 10⁸ cycles.