We consider the nonlocal coupled parabolic system. ut-{increment}u=∫0t(t-s)-γ1|v|p-1v(s)ds,vt-{increment}v=∫0t(t-s)-γ2|u|q-1u(s)ds in (0,T)×Ω when either Ω=RN or Ω⊂RN is a bounded domain with smooth boundary. We assume that 0≤γ1,γ2<1, p,q<1 and the initial data u(0),v(0)∈C0(Ω). We obtain the Fujita critical exponent for the system above which is not given by the scaling argument. © 2010 Elsevier Inc.