The generalized synchronization of different structure chaotic systems based on SETMOS with unknown parameters, double-scroll-like chaotic system and simple piecewise linear chaotic system is investigated with respect to an assumed function. By analyzing characteristics of the chaotic systems and definition of the generalized synchronization, based on Lyapnuov stability theorem, novel and simple adaptive controllers and corresponding parameter update law are proposed for generalized synchronization of different chaotic systems with unknown parameters. Further, if the function is changed, the theory can also be applied for other synchronization for different structure chaotic systems, such as adaptive generalized anti-synchronization. Numerical simulation results are provided to show the effectiveness and feasibility of the proposed theory.