Microfluidic devices provide low sample consumption, high throughput, high integration, and good environment controllability advantages. An alternative to conventional bioreactors, microfluidic devices are a simple and effective platform for stem cell investigations. In this study, we describe the design of a microfluidic device as a chemical and mechanical shear stress bioreactor to stimulate rat bone marrow stromal cells (rBMSCs) into neuronal cells. 1-methyl-3-isobutylxanthine (IBMX) was used as a chemical reagent to induce rBMSCs differentiation into neurons. Furthermore, the shear stress applied to rBMSCs was generated by laminar microflow in the microchannel. Four parallel microfluidic chambers were designed to provide a multiplex culture platform, and both the microfluidic chamber-to-chamber, as well as microfluidic device-to-device, culture stability were evaluated. Our research shows that rBMSCs were uniformly cultured in the microfluidic device and differentiated into neuronal cells with IBMX induction. A three-fold increase in the neuronal cell differentiation ratio was noted when rBMSCs were subjected to both IBMX and fluid flow shear stress stimulation. Here, we propose a microfluidic device which is capable of providing chemical and physical stimulation, and could accelerate neuronal cell differentiation from bone marrow stromal cells.