We report electrohydrodynamic instability in a cholesteric liquid crystal-a inixture of p-methoxy benzylidene p-n-butylaniline (MBBA) and a cholesteric dopant cholesteryl nonanoate (CN), in the presence of a superimposed magnetic field H. We have found a certain intensity H+ with respect to the instability in this mixture with negative dielectric anisotropy, beyond which a stripe pattern appears. With art increasing electric field, the stripe pattern evolves into a grid pattern (GP). Investigations of the H-dependences of thresholds and wavelengths for these patterns in comparison with those of nematic liquid crystals clearly show that the typical GPs found in cholesteric liquid crystals are a superposition of two kinds of stripe patterns induced by the electrohydrodynamic instability.