Axons are very sensitive to molecular gradients and can discriminate extremely small differences in gradient steepness. Microfluidic devices capable of generating chemical gradients and adjusting their steepness could be used to quantify the sensitivity of axonal response. Here, we present a versatile and robust microfluidic device that can generate substrate-bound molecular gradients with evenly varying steepness on a single chip to precisely quantify axonal response. In this device, two solutions are perfused into a central channel via two inlets while partially flowing into two peripheral channels through interconnecting grooves, which gradually decrease the fluid velocity along the central channel. Molecular gradients with evenly and gradually decreased steepness can therefore be generated with a high resolution that is less than 0.05%/mm. In addition, the overall distribution range and resolution of the gradient steepness can be highly and flexibly controlled by adjusting various parameters of the device. Using this device, we quantified the hippocampal axonal response to substrate-bound laminin and ephrin-A5 gradients with varying steepnesses. Our results provided more detailed information on how and to what extent different steepnesses guide hippocampal neuron development during the initial outgrowth. Furthermore, our results show that axons can sensitively respond to very shallow laminin and ephrin-A5 gradients, which could effectively initiate biased differentiation of hippocampal neurons in the steepness range investigated in this study.