A continual learning solution is proposed to address the out-of-distribution generalization problem for pedestrian detection. While recent pedestrian detection models have achieved impressive performance on various datasets, they remain sensitive to shifts in the distribution of the inference data. Our method adopts and modifies Elastic Weight Consolidation to a backbone object detection network, in order to penalize the changes in the model weights based on their importance towards the initially learned task. We show that when trained with one dataset and fine-tuned on another, our solution learns the new distribution and maintains its performance on the previous one, avoiding catastrophic forgetting. We use two popular datasets, CrowdHuman and CityPersons for our cross-dataset experiments, and show considerable improvements over standard fine-tuning, with a 9% and 18% miss rate percent reduction improvement in the CrowdHuman and CityPersons datasets, respectively.