A solid oxide fuel cell stack comprising: a plurality of power generation elements, each of which comprising a fuel electrode, a solid electrolyte, and an air electrode stacked in that order; and an interconnector that electrically connects the air electrode in one of adjacent power generation elements in the plurality of the power generation elements to the fuel electrode in the other power generation element, the plurality of power generation elements being connected in series to each other, wherein an intermediate layer having a porosity of not more than 1% and an electrical conductivity of not less than 0.05 S/cm is provided between the interconnector and the fuel electrode in the other power generation element, in a histogram obtained by an image analysis of a scanning electron microscopic image of the intermediate layer observed with a scanning electron microscope, the porosity is calculated by the following equation: Porosity % = integral value in low − brightness area ÷ integral value of appearance frequency of the whole × 100 the low-brightness area is an area that has a lower brightness than an average of the maximum and the minimum of the brightness, the electrical conductivity is obtained by measuring the electrical conductivity of a specimen by a direct current four-terminal method based on JIS (Japanese Industrial Standards) R 1650-2 under an atmospheric environment at 700°C, the specimen being prepared by subjecting a raw material powder for the interconnector to uniaxial pressing under a load of 900 kgf/cm 2 and firing the pressed product at 1300°C for 2 hours under an atmospheric environment, characterised in that the intermediate layer is formed of a perovskite oxide represented by Sr a La b Ti 1-c-d Nb c Fe d O 3-δ wherein a, b, c, and d are a positive real number that satisfies 0.1 ≤ a ≤ 0.8, 0.1 ≤ b ≤ 0.8, 0.1 ≤ c ≤ 0.3, and 0.3 ≤ d ≤ 0.6, and the content of oxygen (3-δ) is not more than 3.00, the content of the perovskite oxide represented by Sr a La b Ti 1-c-d Nb c Fe d O 3-δ in the intermediate layer is not less than 80% by mole, and the interconnector is formed of a perovskite oxide represented by Sr x La y TiO 3-δ wherein x and y are a positive real number that satisfies 0.8 ≤ x + y ≤ 1.0 and 0.01 < y ≤ 0.1. a plurality of power generation elements, each of which comprising a fuel electrode, a solid electrolyte, and an air electrode stacked in that order; and an interconnector that electrically connects the air electrode in one of adjacent power generation elements in the plurality of the power generation elements to the fuel electrode in the other power generation element, the plurality of power generation elements being connected in series to each other, wherein an intermediate layer having a porosity of not more than 1% and an electrical conductivity of not less than 0.05 S/cm is provided between the interconnector and the fuel electrode in the other power generation element, in a histogram obtained by an image analysis of a scanning electron microscopic image of the intermediate layer observed with a scanning electron microscope, the porosity is calculated by the following equation: Porosity % = integral value in low − brightness area ÷ integral value of appearance frequency of the whole × 100 the low-brightness area is an area that has a lower brightness than an average of the maximum and the minimum of the brightness, the electrical conductivity is obtained by measuring the electrical conductivity of a specimen by a direct current four-terminal method based on JIS (Japanese Industrial Standards) R 1650-2 under an atmospheric environment at 700°C, the specimen being prepared by subjecting a raw material powder for the interconnector to uniaxial pressing under a load of 900 kgf/cm 2 and firing the pressed product at 1300°C for 2 hours under an atmospheric environment, characterised in that the intermediate layer is formed of a perovskite oxide represented by Sr a La b Ti 1-c-d Nb c Fe d O 3-δ wherein a, b, c, and d are a positive real number that satisfies 0.1 ≤ a ≤ 0.8, 0.1 ≤ b ≤ 0.8, 0.1 ≤ c ≤ 0.3, and 0.3 ≤ d ≤ 0.6, and the content of oxygen (3-δ) is not more than 3.00, the content of the perovskite oxide represented by Sr a La b Ti 1-c-d Nb c Fe d O 3-δ in the intermediate layer is not less than 80% by mole, and the interconnector is formed of a perovskite oxide represented by Sr x La y TiO 3-δ wherein x and y are a positive real number that satisfies 0.8 ≤ x + y ≤ 1.0 and 0.01 < y ≤ 0.1.