Abstract: Poincare introduced the continuation method to investigate the existence of periodic solutions in the vicinity of a known periodic solution, a technique that finds widespread applications. In celestial mechanics, it is often observed that there exist more quasi-periodic solutions than periodic solutions. Building upon this insight and incorporating symmetry considerations, we extend the continuation method to explore the existence of quasi-periodic solutions. This study provides examples of the method's applications. Specifically, we examine the existence of quasi-periodic solutions for the Harmonic oscillator and pendulum systems, the figure-eight orbit , and uncover a diverse array of quasi-periodic solutions.