An exhaust gas-purifying catalyst comprising: a substrate; a first catalytic layer facing the substrate and comprising at least one precious metal selected from the group consisting of palladium and platinum and alumina doped with an alkaline-earth metal element, the alkaline-earth metal element substituting for a part of atoms that constitute a crystal lattice of the alumina and/or being positioned in a void between these atoms; and a second catalytic layer facing the substrate with the first catalytic layer interposed therebetween or intervening between the substrate and the first catalytic layer, the second catalytic layer comprising rhodium and alumina doped with an alkaline-earth metal element, and the alkaline-earth metal element substituting for a part of atoms that constitute a crystal lattice of the alumina and/or being positioned in a void between these atoms, wherein a ratio of a total mass of palladium and platinum comprised in the first catalytic layer to a total mass of all precious metals comprised in the first catalytic layer is greater than a ratio of a total mass of palladium and platinum comprised in the second catalytic layer to a total mass of all precious metals comprised in the second catalytic layer, a ratio of a mass of rhodium comprised in the first catalytic layer to a total mass of all precious metals comprised in the first catalytic layer is lower than a ratio of a mass of rhodium comprised in the second catalytic layer to a total mass of all precious metals comprised in the second catalytic layer, a ratio of a total mass of all alkaline-earth metal elements comprised in the first catalytic layer to the total mass of all precious metals comprised in the first catalytic layer is greater than a ratio of a total mass of all alkaline-earth metal elements comprised in the second catalytic layer to the total mass of all precious metals comprised in the second catalytic layer, an alkaline-earth metal element content of the first catalytic layer per volumetric capacity of the substrate is in a range of 0.1 to 50 g/L, and an alkaline-earth element content of the second catalytic layer per volumetric capacity of the substrate is in a range of 0.05 to 10 g/L. a substrate; a first catalytic layer facing the substrate and comprising at least one precious metal selected from the group consisting of palladium and platinum and alumina doped with an alkaline-earth metal element, the alkaline-earth metal element substituting for a part of atoms that constitute a crystal lattice of the alumina and/or being positioned in a void between these atoms; and a second catalytic layer facing the substrate with the first catalytic layer interposed therebetween or intervening between the substrate and the first catalytic layer, the second catalytic layer comprising rhodium and alumina doped with an alkaline-earth metal element, and the alkaline-earth metal element substituting for a part of atoms that constitute a crystal lattice of the alumina and/or being positioned in a void between these atoms, wherein a ratio of a total mass of palladium and platinum comprised in the first catalytic layer to a total mass of all precious metals comprised in the first catalytic layer is greater than a ratio of a total mass of palladium and platinum comprised in the second catalytic layer to a total mass of all precious metals comprised in the second catalytic layer, a ratio of a mass of rhodium comprised in the first catalytic layer to a total mass of all precious metals comprised in the first catalytic layer is lower than a ratio of a mass of rhodium comprised in the second catalytic layer to a total mass of all precious metals comprised in the second catalytic layer, a ratio of a total mass of all alkaline-earth metal elements comprised in the first catalytic layer to the total mass of all precious metals comprised in the first catalytic layer is greater than a ratio of a total mass of all alkaline-earth metal elements comprised in the second catalytic layer to the total mass of all precious metals comprised in the second catalytic layer, an alkaline-earth metal element content of the first catalytic layer per volumetric capacity of the substrate is in a range of 0.1 to 50 g/L, and an alkaline-earth element content of the second catalytic layer per volumetric capacity of the substrate is in a range of 0.05 to 10 g/L.