Large Language Models (LLMs) enhanced with external contexts, such as through retrieval-augmented generation (RAG), often face challenges in handling imperfect evidence. They tend to over-rely on external knowledge, making them vulnerable to misleading and unhelpful contexts. To address this, we propose the concept of context-robust LLMs, which can effectively balance internal knowledge with external context, similar to human cognitive processes. Specifically, context-robust LLMs should rely on external context only when lacking internal knowledge, identify contradictions between internal and external knowledge, and disregard unhelpful contexts. To achieve this goal, we introduce Grft, a lightweight and plug-and-play gated representation fine-tuning approach. Grft consists of two key components: a gating mechanism to detect and filter problematic inputs, and low-rank representation adapters to adjust hidden representations. By training a lightweight intervention function with only 0.0004\% of model size on fewer than 200 examples, Grft can effectively adapt LLMs towards context-robust behaviors.