A continuous steel casting method for producing a strand, the method comprising: pouring molten steel into a continuous casting mold; and simultaneously withdrawing the molten steel while the continuous casting mold is oscillated in a casting direction, wherein the continuous casting mold has a plurality of concave grooves independently formed on an inner wall surface of a mold copper plate in a region extending from a position at least 20 mm above the position of a meniscus in a steady casting state to a position at least 50 mm and at most 200 mm below the position of the meniscus, wherein a plurality of metal-filled portions with different thermal conductivity (19, 19a, 19b, 19c, 20, 20a, 20b, 20c) filled with a metal or a metal alloy having a thermal conductivity that differs by at least 20% from the thermal conductivity of the mold copper plate are disposed in the plurality of concave grooves, wherein the area fraction of the total area of the metal-filled portions with different thermal conductivity (19, 19a, 19b, 19c, 20, 20a, 20b, 20c) relative to the area of the inner wall surface on which the plurality of metal-filled portions with different thermal conductivity (19, 19a, 19b, 19c, 20, 20a, 20b, 20c) are disposed is from 10% to 80% inclusive, wherein a distance and an oscillation mark pitch that is derived from the frequency of oscillation (f) and the speed of casting (Vc) satisfy formula below, wherein a distance satisfies formula below, D 1 ≤ OMP = Vc × 1000 / f D 2 ≤ 4 r wherein, in formula, Vc is the speed of casting (m/min); f is the frequency of oscillation (cpm); OMP is the oscillation mark pitch (mm); and D1 is the distance (mm) between a boundary line between a first one of the plurality of metal-filled portions with different thermal conductivity (19a, 20a) and the mold copper plate and a boundary line between a second one of the metal-filled portions with different thermal conductivity (19b, 20b) and the mold copper plate, the second one of the metal-filled portions with different thermal conductivity (19b, 20b) being located at the same position, with respect to a width direction of the mold copper plate, as the center of gravity of the first one of the metal-filled portions with different thermal conductivity (19a, 20a) and being adjacent to the first one of the metal-filled portions with different thermal conductivity (19a, 20a) in the casting direction, and wherein, in formula, r is the radius (mm) of a circle having a center at the center of gravity of one of the metal-filled portions with different thermal conductivity (19, 19a, 19b, 19c, 20, 20a, 20b, 20c) and having the same area as the one of the metal-filled portions with different thermal conductivity (19, 19a, 19b, 19c, 20, 20a, 20b, 20c), and D2 is the distance (mm) between the center of gravity of the first one of the metal-filled portions with different thermal conductivity (19a, 20a) and the center of gravity of a third one of the metal-filled portions with different thermal conductivity (19c, 20c), the third one of the metal-filled portions with different thermal conductivity (19c, 20c) being disposed at the same position, with respect to the casting direction, as the center of gravity of the first one of the metal-filled portions with different thermal conductivity (19a, 20a) and being adjacent to the first one of the metal-filled portions with different thermal conductivity (19a, 20a) in the width direction. Vc is the speed of casting (m/min); f is the frequency of oscillation (cpm); OMP is the oscillation mark pitch (mm); and D1 is the distance (mm) between a boundary line between a first one of the plurality of metal-filled portions with different thermal conductivity (19a, 20a) and the mold copper plate and a boundary line between a second one of the metal-filled portions with different thermal conductivity (19b, 20b) and the mold copper plate, the second one of the metal-filled portions with different thermal conductivity (19b, 20b) being located at the same position, with respect to a width direction of the mold copper plate, as the center of gravity of the first one of the metal-filled portions with different thermal conductivity (19a, 20a) and being adjacent to the first one of the metal-filled portions with different thermal conductivity (19a, 20a) in the casting direction, and wherein, in formula, r is the radius (mm) of a circle having a center at the center of gravity of one of the metal-filled portions with different thermal conductivity (19, 19a, 19b, 19c, 20, 20a, 20b, 20c) and having the same area as the one of the metal-filled portions with different thermal conductivity (19, 19a, 19b, 19c, 20, 20a, 20b, 20c), and D2 is the distance (mm) between the center of gravity of the first one of the metal-filled portions with different thermal conductivity (19a, 20a) and the center of gravity of a third one of the metal-filled portions with different thermal conductivity (19c, 20c), the third one of the metal-filled portions with different thermal conductivity (19c, 20c) being disposed at the same position, with respect to the casting direction, as the center of gravity of the first one of the metal-filled portions with different thermal conductivity (19a, 20a) and being adjacent to the first one of the metal-filled portions with different thermal conductivity (19a, 20a) in the width direction.