Particle-laden flow through conduits is ubiquitous in both natural and industrial systems. In such flows, particles often migrate across the main fluid stream, resulting in non-uniform spatial distribution owing to particle-fluid and particle-particle interactions. The most relevant lateral particle migration mechanism by particle-fluid interaction is the Segré-Silberberg effect, which is induced by the inertial forces exerted on a particle, as the flow rate increases. However, methods to suppress it have not been suggested yet. Here, we demonstrate that adding a small amount of polymer to the particle-suspending solvent effectively suppresses the Segré-Silberberg effect in a square channel. To accurately determine the position of the particles within the channel cross-sections, we devised a dual-view imaging system applicable to microfluidic systems. Our analyses show that the Segré-Silberberg effect is effectively suppressed in a square microchannel due to the balance between the inertial and elastic forces at an optimal polymer concentration while maintaining nearly constant shear viscosity.