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In this paper, a singular non-Newton polytropic filtration equation under the initial-boundary value condition is revisited. The finite time blow-up results were discussed when the initial energy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>(</mo><msub><mi>u</mi><mn>0</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> was subcritical (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>(</mo><msub><mi>u</mi><mn>0</mn></msub><mo>)</mo><mo><</mo><mi>d</mi></mrow></semantics></math></inline-formula>), critical (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>(</mo><msub><mi>u</mi><mn>0</mn></msub><mo>)</mo><mo>=</mo><mi>d</mi></mrow></semantics></math></inline-formula>), and supercritical (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>(</mo><msub><mi>u</mi><mn>0</mn></msub><mo>)</mo><mo>></mo><mi>d</mi></mrow></semantics></math></inline-formula>), with <i>d</i> being the potential depth by using the potential well method and some differential inequalities. The goal of this paper is to give a finite time blow-up result if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>(</mo><msub><mi>u</mi><mn>0</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> is independent of <i>d</i>. Moreover, the explicit upper bound of the blow-up time is obtained by the classical Levine’s concavity method, and the precise lower bound of the blow-up time is derived by applying an interpolation inequality.