Zn abundances , derived from a model atmosphere analysis of the \lambda 6362.35 Å Zn i line , are presented for 44 thin disk , 10 thick disk and 8 halo dwarf stars in the metallicity range -1.0 < \mbox { [ Fe / H ] } < +0.2 . It is found that [ Zn/Fe ] in thin disk stars shows a slight increasing trend with decreasing metallicity reaching a value \mbox { [ Zn / Fe ] } \simeq +0.1 at \mbox { [ Fe / H ] } = -0.6 . The thick disk stars in the metallicity range -0.9 < \mbox { [ Fe / H ] } < -0.6 have an average \mbox { [ Zn / Fe ] } \simeq +0.15 dex , whereas five alpha-poor and Ni-poor halo stars in the same metallicity range have \mbox { [ Zn / Fe ] } \simeq 0.0 dex . These results indicate that Zn is not an exact tracer of Fe as often assumed in abundance studies of damped Lyman-alpha systems ( DLAs ) . A better understanding of the nucleosynthesis of Zn is needed in order to obtain more detailed information on the past history of star formation in DLAs from e.g . the observed sulphur/zinc ratio .