The occurrence of finite time blow-up phenomenon in the Keller-Segel model with signal consumption has always been a significant area of interest for mathematicians. Unfortunately, there has been limited progress in understanding this phenomenon. In this study, we employ a backward self-similar solution to demonstrate that the finite time blow-up indeed transpires within this model. More precisely, in one-dimensional space, finite time blowing up corresponding to the chemotactic collapse phenomenon (the formation of Dirac $\delta$-singularity) happens; in high-dimensional space, the self-similar solution will blow up everywhere.