Catenary shape profile is a classical type of extended reach well; a nonlinear equation with the initial well oblique angle as unknown factor should be solved for its design. As this unknown factor exists in several triangular functions and logarithmic functions, large amount of calculation is required; and commonused interative solution method is not so ideal. The nonlinear equation is changed to a new one only with logarithmic function and polynomial function, to which geometric analysis is made on the function character, and step search algorithm and adaptive step search algorithm are proposed for solution interval. Numerical solution of new equation can be got rapidly in solution interval by dichotomy. The effectiveness of the above algorithm was proved by the design case of extended reach well, and relationship between hole curvature in arc well section and equation solution was discussed. The algorithm introduced in this paper can be applied in the development of computer software for the design on extended reach well trajectory.