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We construct the global existence and exponential time decay rates of mild solutions to the non-linear Fokker–Planck equation near a global Maxwellians with small-amplitude initial data in the low regularity function space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>L</mi><mi>k</mi><mn>1</mn></msubsup><msubsup><mi>L</mi><mi>T</mi><mo>∞</mo></msubsup><msubsup><mi>L</mi><mi>v</mi><mn>2</mn></msubsup></mrow></semantics></math></inline-formula> where the regularity assumption on the initial data is weaker.