Abstract: In the 3D catenary borehole trajectory design of nonlinear equations numerical algorithm,the coordinates increment of catenary section is calculated by numerical integral.As the numerical integral is nested in the iteration algorithm,the calculation of numerical integral method is the main factor influencing the design equation.Through some math skills,the increment of vertical depth and length increment of horizontal projection have been derived,thus in the design of the equations of iterative algorithm,the numerical integral method can not be taken to calculate vertical and horizontal length increment deep projection.By using integration variable displacement,the integral formula of northern and eastern coordinates is simplified to another equivalent form.With this new kind of numerical calculation,one third of the triangle function number operations can be saved compared with the original save.Thus the iterative algorithm computation efficiency of the whole design equations is obviously improved.