This paper aims to propose a cylindrical magnetorheological fluid brake controlled by shape memory alloy,based on the shape memory effect of shape memory alloy under thermal effect and the rheological behavior of magnetorheological fluid.The shape memory alloy can be used to control the current that induces magnetic field. The Bingham model is used to describe the constitutive characteristics of magnetorheological fluid subject to an applied magnetic field to derive the braking torque equation of cylindrical magnetorheological fluid brake. The expression of the braking time can be obtained from the torqueequilibrium equation of the braked shaft. The relationships of the shape memory alloy switch ’s output displacement with the temperature,the size parameters,the material parameters and the operating load are established based on the shape memory effect. The results indicate that the output displacement of the shape memory alloy switch can change rapidly with the temperature. With the increase of the applied magnetic field strength,the braking torque developed by magnetorheological fluids goes up rapidly,and the braking time is shortened.