Control invariant sets play a key role in model predictive control. Using Lyapunov function,a technique is proposed to design control invariant sets of planar systems in a precise form. First, it is designed for a linear system in Brunovsky canonical form. Then, the result is extended to general linear systems. Finally, the nonlinear control systems are considered, and some sufficient conditions and design techniques are also obtained. Numerical examples are presented to illustrate the proposed design methods.