In the past researches, polymer materials (PDMS, SU-8, PMMA) have proved to be a preferred material for the fabrication of low-noise nanopores. However, it has always been a challenge to fabricate sub-10 nm nanopores on a thin polymer membrane. In this article, we explored a method of fabrication of nanopores on polymethyl methacrylate(PMMA) membrane by the local high electrical field controlled breakdown, which can fast produce sub-2 nm nanopores. Through the improved electric field application method, the nanopore can be fabricated by the instantaneous high electric field 1-7 times higher than the breakdown electric field. The mechanism of the electrical breakdown voltage and current in the formation of nanopores is discussed. Finally, AFM images were also used to characterize the polymer nanopores, which proves the feasibility of fast fabrication method of sub-2 nm low noise polymer nanopores.