A new-type four-dimensional cellular neural network (CNN) is designed, whose piecewise linear function is replaced by smooth continuous function as CNN output module, theoretical analysis proves the new system has chaotic characteristics. By adding two cells, this study generates flux-controlled memristor and creates a brand new six-dimensional memristive CNNs. With the purpose of verifying the validity of this scheme, universal electronic components are adopted to build a memristive module and apply them to the integrity circuit of this system. Multisim circuit simulation software shows that this memristive module has the characteristic of the hysteresis loop as well, and circuit output curves are approximately in agreement with those of MATLAB numerical calculation results within the range of the permitted errors. Finally, via analyses of phase trajectories, equilibrium points, bifurcation diagrams, Lyapunov exponents, and dimension, this study demonstrates that this new type memristive CNNs possesses more abundant dynamic characteristics.