This paper investigates the shadow of slowly rotating Kalb-Ramond (KR) black holes in Lorentz-violating spacetimes. The authors use the slow-rotation approximation to derive first-order rotation series solutions for these black holes. They then analyze the black hole shadow contours under various parameters using numerical backward ray-tracing. The results show that as the Lorentz-violating parameter increases, the apparent size of the black hole shadow decreases, and the effects of rotation, such as the D-shaped structure and frame-dragging, are amplified. Additionally, the KR field enhances gravitational lensing, causing the shadow to occupy a larger area within the photon ring. This distinctive feature can differentiate KR gravity from general relativity. The authors also use the latest observational data from the Event Horizon Telescope (EHT) on M87* and Sgr A* to constrain the Lorentz-violating parameter of rotating KR black holes. They find that rotating black holes allow for the presence of stronger Lorentz violation effects compared to static black holes. The study provides insights into the behavior of black holes in modified gravity theories and highlights the potential for distinguishing between different gravitational theories through observations of black hole shadows. The results suggest that the Lorentz violation parameter is constrained to a narrow range, with values between -0.08 and 0.01 for KR black holes. The study also discusses the implications of these findings for future research in gravitational physics and the potential for new observational signatures of black hole shadows in modified gravity theories.This paper investigates the shadow of slowly rotating Kalb-Ramond (KR) black holes in Lorentz-violating spacetimes. The authors use the slow-rotation approximation to derive first-order rotation series solutions for these black holes. They then analyze the black hole shadow contours under various parameters using numerical backward ray-tracing. The results show that as the Lorentz-violating parameter increases, the apparent size of the black hole shadow decreases, and the effects of rotation, such as the D-shaped structure and frame-dragging, are amplified. Additionally, the KR field enhances gravitational lensing, causing the shadow to occupy a larger area within the photon ring. This distinctive feature can differentiate KR gravity from general relativity. The authors also use the latest observational data from the Event Horizon Telescope (EHT) on M87* and Sgr A* to constrain the Lorentz-violating parameter of rotating KR black holes. They find that rotating black holes allow for the presence of stronger Lorentz violation effects compared to static black holes. The study provides insights into the behavior of black holes in modified gravity theories and highlights the potential for distinguishing between different gravitational theories through observations of black hole shadows. The results suggest that the Lorentz violation parameter is constrained to a narrow range, with values between -0.08 and 0.01 for KR black holes. The study also discusses the implications of these findings for future research in gravitational physics and the potential for new observational signatures of black hole shadows in modified gravity theories.