This paper presents a study of the optical and thermodynamic properties of an Euler-Heisenberg (EH) black hole surrounded by perfect fluid dark matter (PFDM). A new metric for static spherically symmetric spacetime is derived, which describes the EH black hole in the presence of PFDM. The metric is constructed by combining the EH black hole solution with the PFDM solution, leading to a modified spacetime geometry that incorporates the effects of dark matter. The optical properties of the black hole are analyzed by studying the photon orbits and the image of a thin accretion disk. The results show that the radius of the black hole shadow increases with the strength of the dark matter effect. Additionally, stronger dark matter reduces the light intensity of the accretion disk. The Doppler effect is also considered, which influences the brightness distribution of the disk. In the thermodynamic analysis, the black hole is studied in the context of anti-de Sitter (AdS) space. The thermodynamic properties, including mass, temperature, entropy, and pressure, are calculated. The study reveals that the number of critical points of the black hole depends on the quantum electrodynamic (QED) parameter. When the QED parameter is positive, a critical value of the dark matter parameter determines the number of critical points. The paper also investigates phase transitions and critical points of the black hole in the extended thermodynamic framework. The critical points are determined by the conditions of second-order phase transitions, and the results show that the critical value of the dark matter parameter can lead to the merging of two critical points into one. The study provides insights into the influence of dark matter on black hole physics and highlights the importance of considering both QED effects and dark matter in understanding black hole thermodynamics and optical properties. The results suggest that future experiments could help distinguish between the effects of QED and dark matter on black hole behavior.This paper presents a study of the optical and thermodynamic properties of an Euler-Heisenberg (EH) black hole surrounded by perfect fluid dark matter (PFDM). A new metric for static spherically symmetric spacetime is derived, which describes the EH black hole in the presence of PFDM. The metric is constructed by combining the EH black hole solution with the PFDM solution, leading to a modified spacetime geometry that incorporates the effects of dark matter. The optical properties of the black hole are analyzed by studying the photon orbits and the image of a thin accretion disk. The results show that the radius of the black hole shadow increases with the strength of the dark matter effect. Additionally, stronger dark matter reduces the light intensity of the accretion disk. The Doppler effect is also considered, which influences the brightness distribution of the disk. In the thermodynamic analysis, the black hole is studied in the context of anti-de Sitter (AdS) space. The thermodynamic properties, including mass, temperature, entropy, and pressure, are calculated. The study reveals that the number of critical points of the black hole depends on the quantum electrodynamic (QED) parameter. When the QED parameter is positive, a critical value of the dark matter parameter determines the number of critical points. The paper also investigates phase transitions and critical points of the black hole in the extended thermodynamic framework. The critical points are determined by the conditions of second-order phase transitions, and the results show that the critical value of the dark matter parameter can lead to the merging of two critical points into one. The study provides insights into the influence of dark matter on black hole physics and highlights the importance of considering both QED effects and dark matter in understanding black hole thermodynamics and optical properties. The results suggest that future experiments could help distinguish between the effects of QED and dark matter on black hole behavior.