Solute transport in a narrow space is the most elemental process in chromatography and biological pattern formation. However, the observation of such transport has been quite difficult, and theoretical investigations have therefore preponderated. Here, using a space- and time-resolved surface plasmon resonance (SPR) method, we measured the nanoscale near-wall (next to the wall) transport rate in a narrow channel after a solution and its solvent had come into contact. By combining the SPR method with a capillary injection method, which enables two solution plugs to flow immediately after they have made contact, we were able to measure the solute concentration evolution at the channel wall. We tested three combinations of two plugs of solution-water-glucose, sodium chloride-water, and glucose-sodium chloride-and succeeded in measuring diffusion-coefficient-dependent changes in the concentration of solute flowing through a rectangular microchannel in less than 0.4 s. A numerical analysis of this system revealed the acceleration of the solute/solution boundary moving on the wall and its deceleration at the center of the channel cross section. The observed experimental transport rate agreed with the numerical result quantitatively. These results show that the solute transport followed a laminar flow with a no-slip model and that the molecules were transported in the order of their diffusivity. In the third combination, when the two solutions made contact and started flowing, the interdiffusion of the solutes resulted in temporal concentrations lower than either of the solutions before contact, which indicated that the contact between the two solutions quickly led to separation by the advection-diffusion processes. We found that such a concentration profile could actually be measured. Our techniques are simple and applicable to a wide range of molecules; the method opens the way to direct observation of the space-time near-wall solute transport process and can be used for the rapid determination of diffusivity.