Metal–insulator transition in the ground state of the Hubbard chain with the next-nearest-neighbor hopping is studied by exact diagonalization method. This model shows the partially ferromagnetic metal near the Mott insulator for large Coulomb repulsion while the model reveals the non-magnetic metal for small but finite Coulomb repulsion. We find the transition between the partially ferromagnetic metal and the Mott insulator without phase separation. A new critical exponent of the diverging charge compressibility with respect to the hole density is observed when the system approaches the metal–Mott-insulator transition point from the side of the partially ferromagnetic metal. We also find the occurrence of the phase separation between partially ferromagnetic metal and the Mott insulator for even larger Coulomb repulsion. The model proposed here is interesting in view of the magnetism as well as the metal–insulator transition.