Thermal and flow characteristics of a channel formed by circular tube bank fins stamped with convex/concave pyramids were numerically investigated by ANSYS Fluent software, and the parametric studies on the thermal performance of the pyramid fin are examined for varying pyramid height (H p), pyramid length (L p), and pyramid width (W p) as Reynolds number (Re) ranged from 1297 to 4541. The pyramid fin provides superior thermal performance to the counterpart plain fin, which is ascribed to the punched pyramids effectively expanding heat transfer area and inducing the secondary flow to better fluid mixing, and the action of the convex/concave pyramids lead to the area of undesirable heat transfer dead zone behind the circular tube being significantly reduced. Under identical pumping power constraint, the thermal performance factor of 1.41 is achieved for H p = 1 mm, L p = 5.74 mm, and W p = 3 mm at Re = 3892, and the optimal pyramid height and width fin respectively are H p = 1 mm and W p = 3 mm for studied cases, while the optimal pyramid length is associated closely with Re. The correlations of average Nusselt number and friction factor are proposed to estimate thermal performance of the pyramid fin used in a finned circular tube heat exchanger.