Robots need task planning methods to achieve goals that require more than individual actions. Recently, large language models (LLMs) have demonstrated impressive performance in task planning. LLMs can generate a step-by-step solution using a description of actions and the goal. Despite the successes in LLM-based task planning, there is limited research studying the security aspects of those systems. In this paper, we develop Robo-Troj, the first multi-trigger backdoor attack for LLM-based task planners, which is the main contribution of this work. As a multi-trigger attack, Robo-Troj is trained to accommodate the diversity of robot application domains. For instance, one can use unique trigger words, e.g., "herical", to activate a specific malicious behavior, e.g., cutting hand on a kitchen robot. In addition, we develop an optimization method for selecting the trigger words that are most effective. Through demonstrating the vulnerability of LLM-based planners, we aim to promote the development of secured robot systems.