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In this paper, we determine the Fujita critical exponent of the following time fractional subdiffusion equation with nonlinear memory 0CDtαu−△u=0It1−γ|u|p−1u,x∈RN,t>0,u(0,x)=u0(x),x∈RN,where 0 < α < 1, 0 ≤ γ < 1, γ ≤ α, p > 1, u0∈C0RN, 0It1−γ denotes left Riemann‐Liouville fractional integral of order 1 − γ. Let β = 1 − γ. We prove that, if 1 p∗ and ‖u0‖LqcRN is sufficiently small, where qc=Nα(p−1)2(α+β), then u exists globally. [ABSTRACT FROM AUTHOR]