Abstract A model on the Rayleigh-Benard problem of a non-ideal MHD flow in a sheared magnetic field is proposed and studied. A new set of nonlinear differential equations for the model bas been derived. Theoretical and numerical analysis shows that the set of equations implies a strange attractor with several novel features differing from Lorenz attractor and, in particular, the coexistence of all three routes to chaos in that model. Among the well-known models with these routes, so far, our system of equations is the unique one without any extrinsic periodic driving term. It exhibits more immediately the intrinsic stochasticity of deterministic nonlinear system. The stochastic motion and reconnection of magnetic field-lines, and the creation of magnetic islands are observed in numerical simulating of this set of equations.