Antimicrobial peptides (AMPs) are potent drug candidates against microbes such as bacteria, fungi, parasites, and viruses. The size of AMPs ranges from less than ten to hundreds of amino acids. Often only a few amino acids or the critical regions of antimicrobial proteins matter the functionality. Accurately predicting the AMP critical regions could benefit the experimental designs. However, no extensive analyses have been done specifically on the AMP critical regions and computational modeling on them is either non-existent or settled to other problems. With a focus on the AMP critical regions, we thus develop a computational model AMPcore by introducing a state-of-the-art machine learning method, conditional random fields. We generate a comprehensive dataset of 798 AMPs cores and a low similarity dataset of 510 representative AMP cores. AMPcore could reach a maximal accuracy of 90% and 0.79 Matthew's correlation coefficient on the comprehensive dataset and a maximal accuracy of 83% and 0.66 MCC on the low similarity dataset. Our analyses of AMP cores follow what we know about AMPs: High in glycine and lysine, but low in aspartic acid, glutamic acid, and methionine; the abundance of α-helical structures; the dominance of positive net charges; the peculiarity of amphipathicity. Two amphipathic sequence motifs within the AMP cores, an amphipathic α-helix and an amphipathic π-helix, are revealed. In addition, a short sequence motif at the N-terminal boundary of AMP cores is reported for the first time: arginine at the P(-1) coupling with glycine at the P1 of AMP cores occurs the most, which might link to microbial cell adhesion.