We propose and demonstrate a new magneto-optical trap (MOT) for alkaline-earth-metal-like (AEML) atoms where the narrow $^{1}S_{0}rightarrow$$^{3}P_{1}$ transition and the broad $^{1}S_{0}rightarrow$$^{1}P_{1}$ transition are spatially arranged into a core-shell configuration. Our scheme resolves the main limitations of previously adopted MOT schemes, leading to a significant increase in both the loading rate and the steady state atom number. We apply this scheme to $^{174}$Yb MOT, where we show about a hundred-fold improvement in the loading rate and ten-fold improvement in the steady state atom number compared to reported cases that we know of to date. This technique could be readily extended to other AEML atoms to increase the statistical sensitivity of many different types of precision experiments.