It is the purpose of the present paper to introduce an approach based on the homotopy analysis method to solve the nonlinear initial or boundary value problems with strongly nonlinear terms like (sqrt root, exp, sinh, cos,…). This approach reduces time consuming in the homotopy analysis method. Advantage of proposed idea is solving the problems without any transformation or approximation. The Sine-Gordon equation and some examples are used as illustrative examples to show the simplicity and effectiveness of the proposed approach. Also we solve the first extension of Bratu problem to show the proposed approach is capable to predict and calculate all branches of the solutions simultaneously.