Circulating tumor cells (CTCs) are metastatic cells that are responsible for commencing cancer metastases. By detecting and analyzing CTCs, early cancer can be diagnosed and a proper treatment plan can be determined. For fabricating a highly efficient and high throughput deformation-based CTC filtration micro-channel, more researches on CTC deformation through micro-channel are required for an extensive understanding of cell behavior. Numerical simulation offers us an easy way to interpret the cell behavior throughout deformation. To understand the effect of shear-thinning characteristics of the cell, a non-Newtonian liquid droplet cell model is adopted while analyzing the deformation process of CTC through a micro-channel with non-uniform cross-sections. Pressure signatures, cell deformations, and streamlines are studied thoroughly to understand the flow dynamics of the non-Newtonian cell passing process while undergoing deformation. Critical pressure and viscosity-induced pressure are scrutinized at different flow rates. It is found that the non-Newtonian cell model shows a similar pattern of pressure signature regardless of increasing flow rate. The present study shows that the critical pressure locations for non-Newtonian and Newtonian cell models are distinct at high flow rates. Finally, a modified empirical formula is proposed for viscosity-induced pressure to consider the effects of the interaction between the non-Newtonian cell and blood. These findings will provide significant insights into the non-Newtonian cell passing process through a conical micro-channel while squeezing, and consequential guidance for optimizing highly efficient and high throughput deformation-based CTC filtering microchip.