Generation of concentration gradients of reactive molecules is of fundamental importance for many applications including biology, pharmaceutical and chemical engineering. By numerically simulating the flow behaviour, we reveal the possible factors that cause significant error in the gradients generated by the conventional universal microfluidic gradient generator (MGG) device reported previously. Based on these computational analyses, we optimize the geometrical design of the conventional 2-inlet MGG devices and improve the accuracy of the generated gradients. Moreover, we innovatively propose a 3-inlet MGG design showing desirable accuracy and versatility on creating various gradient profiles using the one single device. We further demonstrate our numerical simulation by fabricating the MGG devices by soft lithography and experimentally produce concentration gradients of diverse power functions. In general, the current study substantially improves the performance of universal MGG devices, which can serve as powerful tools for widespread applications in biology and chemistry.