Achieving generalization in one-shot imitation learning (OSIL) is crucial for deploying the imitator agents in dynamic environments where unexpected changes can occur after demonstration. This scenario, when deployed, would inevitably lead agents to face situations unseen in the provided demonstrations, thus asking for a higher level of generalization ability for the imitator policy. While traditional OSIL methods excel in relatively stationary settings, their adaptability to such unforeseen changes is limited. In this work, we present a new algorithm called Deep Demonstration Tracing (DDT). DDT leverages a specialized neural network architecture to encourage agents to adaptively trace suitable states in demonstrations. Besides, it integrates OSIL into a meta-reinforcement-learning training paradigm, providing regularization for policies in unexpected situations. We evaluate DDT on a new navigation task suite and robotics tasks, demonstrating its superior performance over existing OSIL methods across all evaluated tasks in dynamic environments with unforeseen changes.