In this article, a magnetorheological elastomer peristaltic pump capable of bidirectionally conveying Newtonian and non-Newtonian fluids with precise net pumped volume and required viscosity patterns of fluids is presented and numerically investigated. The basic element is very succinct, which is composed of only a magnetorheological elastomer tube and an electromagnet. T wo basic elements in series constitute a magnetorheological elastomer peristaltic pump. The maximum pumped volume can be achieved using maximum lag between voltage parameters gap1 and gap2. The Nelder–Mead optimization method is applied to realize the precise control of the net pumped volume during a steady working cycle. For a certain net pumped volume, the viscosity of fluids can also be adjusted through the modulation of the driving voltage parameters obtained from the Nelder–Mead optimization method.