The present study is aimed at numerical investigation, by using conjugated heat transfer approach, of the effect of different types of rectangular fins (outer zigzag-inner zigzag-flat-outer zigzag (type B) and inner zigzag-flat-inner zigzag (type C)), which are mounted on a flat plate channel having three-dimensional rectangular cross section, on heat transfer enhancement in a plate fin heat exchanger. The numerical computations are performed by solving a steady, three-dimensional Navier-Stokes equation and an energy equation by using the FLUENT soft ware program. Air is taken as a working fluid. The study is carried out at Re = 400, at the inlet temperatures and velocities of cold and hot air fixed at 300 K, 600 K and 1.338 m/s, 0.69 m/s, respectively. The results show that the heat transfer is increased by 9 percent at the exit of channel with the fin type C, when compared to a channel without a fin with counterflow. The effect exerted on heat transfer enhancement by different values of the Reynolds number and fin heights, and also by temperature distributions on the hot and cold fluid sides of the channel surface are investigated in the case of parallel flow and counterflow.