Quasinormal modes of Dirac field in the background of a non-Schwarzschild black holes in theories with higher curvature corrections are investigated in this paper. With the help of the semi-analytic WKB approximation and further using of Padé approximants as prescribed in Matyjasek and Opala (Phys Rev D 96(2):024011. [gr-qc], 2017) we consider quasinormal modes of a test massless Dirac field in the Einstein-Dilaton-Gauss-Bonnet (EdGB) and Einstein-Weyl (EW) theories. Even though the effective potential for one of the chiralities has a negative gap we show that the Dirac field is stable in both theories. We find the dependence of the modes on the new dimensionless parameter p (related to the coupling constant in each theory) for different values of the angular parameter l and show that the frequencies tend to linear dependence on p. The allowed deviations of qausinormal modes from their Schwarzschild limit are one order larger for the Einstein-Weyl theory than for the Einstein-Dilaton-Gauss-Bonnet one, achieving the order of tens of percents. In addition, we test the Hod conjecture which suggests the upper bound for the imaginary part of the frequency of the longest lived quasinormal modes by the Hawking temperature multiplied by a factor. We show that in both non-Schwarzschild metrics the Dirac field obeys the above conjecture for the whole range of black-hole parameters.