A new boundary condition treatment at the pseudo-outer boundary is proposed to numerically simulate the laminar natural convection heat transfer around a horizontal finned tube. It may be implemented easily while largely reducing the computational domain size. Numerical tests indicate that by using this boundary condition, the relative errors of the average Nusselt number of the laminar natural convection around a horizontal isothermal cylinder are less than 0.5% when compared with the benchmark solutions. The heat transfer of the laminar natural convection around a horizontal compound tube with different fin heights and a different number of fins are calculated using the conjugated computational method with primitive variables. The key findings are as follows: ( 1) for a fixed fin number, there exists an optimum relative fin height at which the total heat transfer rate of the finned tube approaches the maximum; (2) for a fixed relative fin height, there exists an optimum fin number at which the total heat transfer rate of the finned tube reaches its maximum; and (3) the tube fin positioning also has some effect on the heat transfer. Positioning a pair of fins in the vertical symmetric plane will deteriorate the overall heat transfer to some extent.