The trilayer nickelate Nd4Ni3O 10−δ (δ ≈ 0.15) was investigated by the measurements of x-ray diffraction, electrical resistivity, magnetic susceptibility, and heat capacity. The crystal structure data suggest a higher Ni valence in the inner perovskite-like layer. At ambient pressure the resistivity shows a jump at 162 K, indicating a metal-to-metal transition (MMT). The MMT is also characterized by a magnetic susceptibility drop, a sharp specific-heat peak, and an isotropic lattice contraction. Below ∼ 50 K, a resistivity upturn with a logT dependence shows up, accompanying with a negative thermal expansion. External hydrostatic pressure suppresses the resistivity jump progressively, coincident with the diminution of the logT behavior. The low-temperature electronic specific-heat coefficient is extracted to be ∼ 150 mJ K −2 mol-fu −1 , equivalent to ∼ 50 mJ K −2 mol-Ni −1 , indicating an unusual heavy-electron correlated state. The novel heavy-electron state as well as the logarithmic temperature dependence of resistivity is explained in terms of the Ni 3+ centered Kondo effect in the inner layer of the (NdNiO3)3 trilayers.