Through introducing a generalized memristor and an LC absorbing network into Wien-bridge oscillator, a kind of memristive Wien-bridge chaotic oscillator is proposed. The dynamical model of the memristive Wien-bridge chaotic oscillator is established, based on which the equilibrium points and their stabilities are studied and the dynamical behaviors are further analyzed when the circuit element parameters are varied. The research findings indicate that the memristive Wien-bridge chaotic oscillator has three determinative equilibrium points and their stabilities depend on the circuit element parameters, and that there exist complex nonlinear phenomena including periodic oscillations, chaotic oscillations and fast-slow effects when the parameters are changed. The experimental circuit is simple and easy to realize. The experimental waveforms and numerical simulations are consistent with each other, which well verify the theoretical analyses.