The trajectory of cycloid extended reach well consists of straight section-arc section-cycloid section-steady inclined section with the minimum or very small friction and friction moment. The design comes down to solution for system of two elements equations, when the unknown design parameters are according to the initial well deviation angle of cycloid section or deviation angle of remained inclined section, the equations are nonlinear without analytical solution. The equivalent triangle function equation is obtained by mathematical transformation and simplification; numerical iterative algorithm for triangle function equation approximate solution is put forward by interval query and bisection method. The numerical examples show the algorithm has high calculation accuracy and quick operation with good iterative stability. This new algorithm can be applied in the development of computer software to improve the applicability.