The surface heat transfer coefficient of laminar flow rhrough a rectangular pipe under a constant heat flux boundary condition is discussed in this paper.The coefficient decreases with the increase of the pipe length at first and then reaches a relative constant value.This distribution profile is similar to the convection of laminar flow over a plane very much.The mean velocity affects surface heat transfer coefficient especially at the entrance stage.An approximate formula about these is put forward by using the Least-squares method.The heat flux has no effect on the convection.