A building exterior insulation structure, comprising: a first board member disposed on an exterior side of a framework forming a building, the first board member extending in a first direction and a second direction substantially perpendicular to the first direction; a plurality of first supporting members disposed on the exterior side of the first board member; at least one first thermal insulator disposed on the exterior side of the first board member and between the first supporting members; a plurality of second supporting members (82; 282) disposed on the exterior side of the first supporting members, the second supporting members (82; 282) extending in the first direction and being spaced apart from one another in the second direction; and at least one second thermal insulator disposed on the exterior side of the first thermal insulator and between the second supporting members (82; 282); a plurality of securing members fixed to the exterior side of the second supporting members (82; 282) and extending in the second direction; and a plurality of exterior wall members (2; 202) attached to the securing members to cover the framework, wherein the exterior wall members (2; 202) adjacent to each other are joined together without leaving a gap therebetween, wherein a length of each securing member in the second direction is determined so as to be long enough to be fixable to at least two of the second supporting members (82; 282) and so as to be shorter than a length of each exterior wall member (2; 202) in the second direction, wherein a first gap (W1; W21) is left between each two of the securing members adjacent to each other in the second direction, the first gap (W1; W21) falling within a range of approximately 10 mm to 300 mm, and wherein at least part of each second supporting member (82; 282) is made of a material having a thermal conductivity lower than that of steel. a first board member disposed on an exterior side of a framework forming a building, the first board member extending in a first direction and a second direction substantially perpendicular to the first direction; a plurality of first supporting members disposed on the exterior side of the first board member; at least one first thermal insulator disposed on the exterior side of the first board member and between the first supporting members; a plurality of second supporting members (82; 282) disposed on the exterior side of the first supporting members, the second supporting members (82; 282) extending in the first direction and being spaced apart from one another in the second direction; and at least one second thermal insulator disposed on the exterior side of the first thermal insulator and between the second supporting members (82; 282); a plurality of securing members fixed to the exterior side of the second supporting members (82; 282) and extending in the second direction; and a plurality of exterior wall members (2; 202) attached to the securing members to cover the framework, wherein the exterior wall members (2; 202) adjacent to each other are joined together without leaving a gap therebetween, wherein a length of each securing member in the second direction is determined so as to be long enough to be fixable to at least two of the second supporting members (82; 282) and so as to be shorter than a length of each exterior wall member (2; 202) in the second direction, wherein a first gap (W1; W21) is left between each two of the securing members adjacent to each other in the second direction, the first gap (W1; W21) falling within a range of approximately 10 mm to 300 mm, and wherein at least part of each second supporting member (82; 282) is made of a material having a thermal conductivity lower than that of steel.