Abstract: The integral relational expression is adopted to solve the flat plate laminar boundary layer problem, on the basis of meeting the basic boundary conditions, a Jacobin elliptic sine function is proposed as a new approximate velocity distribution function, using the method of least squares to determine the undetermined coefficient. The velocity profile is in good agreement with the exact solutions corresponding to the boundary layer differential equations. The new distribution function is characteristic of a high accuracy and simpler in form, which is easy for use in engineering application.