This paper deals with the critical blow-up and extinction exponents for the non-Newton polytropic filtration equation. We reveals a fact that the equation admits two critical exponents

) with

. In other words, when q belongs to different intervals (0,

), the solution possesses complete different properties. More precisely speaking, as far as the blow-up exponent is concerned, the global existence case consists of the interval (0,

]. However, when q

), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval (

), while for q

), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q =

is concerned, the other parameter

will play an important role. In other words, when

belongs to different interval (0,

) or (

,+

), where

is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely different properties.