A flow control honeycomb structure for use in an intake passage of an engine for producing turbulent flow in an air-fuel mixture flowing through the intake passage, which structure includes a short cylindrical peripheral wall defining therein a circular passage having a substantially circular cross section, a plurality of substantially crisscross partitions joined to and disposed in the peripheral wall and dividing the circular passage into a first group of square passageways each having a substantially square cross section and a second group of four triangular passageways each having a substantially triangular cross section and a relatively large cross-sectional area, and a plurality of ribs extending obliquely from joints of those of the passageways which define the triangular passageways radially outwardly to the peripheral wall through the triangular passageways to divide each of the triangular passageways into a plurality of subpassageways of substantially the same cross-sectional area as the square passages. The square and triangular passageways are progressively narrower downstream in the direction in which the air-fuel mixture flow through the intake passage. A method of making the flow control honeycomb structure molding without producing burrs and ridges in any portion of the final honeycomb structure is also disclosed.