In this paper, the effect of stochastic magnetic field (s. m. f.) on the eigen-modes of low frequency drift wave is analysed. We show that the existence of s. m. f. can affect the response of electrons to the wave, so that the electron dispersion function varies. In the vicinity of the rational magnetic surface (where k‖≈0), the variation is particularly significant. The s. m. f. can make the electron dispersion function considerably smoother, and the change in electron dispersion function may greatly affect the stability of the eigen-modes of drift wave. It is shown that if the s. m. f. is strong enough (but still within the region achievable experimentally), the so-called universal modes of drift wave may become absolutly unstable.