This paper presents a method to generate a new metric for static spherically symmetric space-time, which is used to construct a metric describing an Euler-Heisenberg (EH) black hole surrounded by perfect fluid dark matter (PFDM). The authors investigate the optical and thermodynamic properties of this system. They find that the radius of the shadow increases with the intensity of dark matter, and stronger dark matter reduces the light intensity of the accretion disk. In thermodynamics, when the quantum electrodynamic (QED) parameter is positive, there is a critical value of the dark matter parameter that determines the number of critical points of the black hole. The study also explores the phase transition and critical points in the extended thermodynamic framework, showing that the critical points are influenced by the dark matter parameter. The results highlight the impact of dark matter on the physics of black holes and provide insights into the mechanism of dark matter in gravity theories.This paper presents a method to generate a new metric for static spherically symmetric space-time, which is used to construct a metric describing an Euler-Heisenberg (EH) black hole surrounded by perfect fluid dark matter (PFDM). The authors investigate the optical and thermodynamic properties of this system. They find that the radius of the shadow increases with the intensity of dark matter, and stronger dark matter reduces the light intensity of the accretion disk. In thermodynamics, when the quantum electrodynamic (QED) parameter is positive, there is a critical value of the dark matter parameter that determines the number of critical points of the black hole. The study also explores the phase transition and critical points in the extended thermodynamic framework, showing that the critical points are influenced by the dark matter parameter. The results highlight the impact of dark matter on the physics of black holes and provide insights into the mechanism of dark matter in gravity theories.