This paper presents the construction of rotating black hole solutions with a cosmological constant in the scalar-tensor-vector gravity (STVG) theory, known as Kerr-MOG-(A)dS black holes. These solutions incorporate a gravitational charge as a source, modifying the gravitational constant to $ G = G_{\mathrm{N}}(1 + \alpha) $. The study investigates the effects of the MOG parameter $ \alpha $ and the cosmological constant $ \Lambda $ on the black hole shadow, which is shaped by light propagation in spacetime. As $ \Lambda $ increases, the apparent size of the black hole shadow decreases, while the shadow expands with increasing $ \alpha $, reaching a maximum at a certain value. The shadow becomes more rounded with higher rotation parameters, leading to degeneracy between different black hole parameters. However, numerical ray-tracing techniques show that gravitational lensing and frame-dragging effects distinguish this degeneracy. The Kerr-MOG-dS spacetime has an observer located within the domain of outer communication, not at infinity. The shadow's apparent shape and distortions are analyzed, with the angular radius $ R_s $ and distortion parameter $ \delta_s $ used to characterize the shadow. The results show that $ R_s $ increases with $ \alpha $ for small $ \Lambda $, reaching a maximum at $ \alpha \approx 1.815 $ for $ \Lambda = 10^{-3} $. The distortion $ \delta_s $ decreases with increasing $ \alpha $, indicating less deformation of the shadow. The inclusion of the cosmological constant provides a larger parameter space for the MOG parameters. The study also calculates the angular radius of the black hole shadow for Sgr A* and M87* using the Kerr-MOG-dS metric, showing that the theoretical model is consistent with recent observational data. The results suggest that the interplay between the cosmological constant and MOG parameter leads to intriguing phenomena in the black hole shadow contours. Future research could explore other observable measurements of the shadow and the properties of the Kerr-MOG-AdS black hole, including thermodynamics, topological classification, and phase transitions.This paper presents the construction of rotating black hole solutions with a cosmological constant in the scalar-tensor-vector gravity (STVG) theory, known as Kerr-MOG-(A)dS black holes. These solutions incorporate a gravitational charge as a source, modifying the gravitational constant to $ G = G_{\mathrm{N}}(1 + \alpha) $. The study investigates the effects of the MOG parameter $ \alpha $ and the cosmological constant $ \Lambda $ on the black hole shadow, which is shaped by light propagation in spacetime. As $ \Lambda $ increases, the apparent size of the black hole shadow decreases, while the shadow expands with increasing $ \alpha $, reaching a maximum at a certain value. The shadow becomes more rounded with higher rotation parameters, leading to degeneracy between different black hole parameters. However, numerical ray-tracing techniques show that gravitational lensing and frame-dragging effects distinguish this degeneracy. The Kerr-MOG-dS spacetime has an observer located within the domain of outer communication, not at infinity. The shadow's apparent shape and distortions are analyzed, with the angular radius $ R_s $ and distortion parameter $ \delta_s $ used to characterize the shadow. The results show that $ R_s $ increases with $ \alpha $ for small $ \Lambda $, reaching a maximum at $ \alpha \approx 1.815 $ for $ \Lambda = 10^{-3} $. The distortion $ \delta_s $ decreases with increasing $ \alpha $, indicating less deformation of the shadow. The inclusion of the cosmological constant provides a larger parameter space for the MOG parameters. The study also calculates the angular radius of the black hole shadow for Sgr A* and M87* using the Kerr-MOG-dS metric, showing that the theoretical model is consistent with recent observational data. The results suggest that the interplay between the cosmological constant and MOG parameter leads to intriguing phenomena in the black hole shadow contours. Future research could explore other observable measurements of the shadow and the properties of the Kerr-MOG-AdS black hole, including thermodynamics, topological classification, and phase transitions.