A method was developed for the rapid and quantitative analysis of 30 veterinary drugs belonging to 17 classes (amphenicols (1), anthelmintics (1), cephalosporins (4), coccidiostats (1), lincosamides (1), macrolide (1), nitroimidazole (1), penicillins (3), phenylhydrazines (1), polypeptides (1), pyrethrins (1), quinolones (5), sulfonamides (3), tetracycline (3), neuroleptic agents (1), triazene trypanocidal agents (1), other. (1)) in feeds. The proposed method with a modified Quick Polar Pesticides (QuPPe) sample preparation was validated for the determination of 30 veterinary drugs in feed samples by liquid chromatography triple-quadrupole mass spectrometry (LC–MS/MS). The sample was extracted with methanol containing 1% acetic acid and purified by dispersive solid-phase extraction (d-SPE) with C18. Good linearity (r2 ≥ 0.98) was observed, and the LOQ values ranged from 10 to 200 µg/kg. Average recoveries ranged from 70.8 to 118.4%, and the relative standard deviation was ≤ 18.7%. This validated method was used in the determination of 30 veterinary drugs in 142 feed samples obtained from South Korea. The results show that lincomycin was present in only one of the tested feed samples, although it was detected at a value lower than the LOQ. In conclusion, this multi-residue method can be used for screening through the detection and quantitation of residual multiclass veterinary drugs in feed samples.