The guidance vector field encoding problem is revisited via exploiting the recently developed differential Lyapunov framework for contraction analysis. In control applications, a designed guidance vector field is utilized to guide a particle (such as a robot, or an end actuator) to converge to and circulate along a target curve, such as robot navigation, or motion planing. This paper proposes some new methods for guidance vector filed encoding. The methods analyze the guidance vector field encoding problem from a theoretical perspective providing insights into the problem, and it shows that the contraction analysis is a natural theoretical tool for guidance vector encoding. Furthermore, the differences and relations between the proposed result and the previous methods are discussed. Simulation examples are presented to illustrate the effectiveness of the proposed methods.