This paper presents an iterative algorithm for solving intuitionistic fuzzy nonlinear equations (IFNEs). The proposed method is based on the classical conjugate gradient (CG) search direction. An interesting feature of the new algorithm is that it considers problems based on the special triangular intuitionistic fuzzy number. For this purpose, intuitionistic fuzzy quantities are transformed into membership and non-membership parametric forms, and a line search procedure is employed to compute the step length. Preliminary results from numerical experiments are presented to demonstrate the performance of the method. It is observed that the proposed hybrid CG method is highly effective and promising. KEYWORDS Hybrid CG, intuitionistic fuzzy nonlinear equation, parametric form, step length, inexact line search