The hydrogen isotope effect on the Dimits shift in drift wave turbulence (Dimits et al 2000 Phys. Plasmas7 969) is discussed using the theory of zonal flows, in which the nonlinear damping rate of zonal flows is taken into account. The up-shift of the critical linear growth rate of the drift waves, above which drift wave fluctuations develop, is investigated. The dependence on the mass number of the hydrogen isotope is discussed.