Efficient and robust task planning for a human-robot collaboration (HRC) system remains challenging. The human-aware task planner needs to assign jobs to both robots and human workers so that they can work collaboratively to achieve better time efficiency. However, the complexity of the tasks and the stochastic nature of the human collaborators bring challenges to such task planning. To reduce the complexity of the planning problem, we utilize the hierarchical task model, which explicitly captures the sequential and parallel relationships of the task. We model human movements with the sigma-lognormal functions to account for human-induced uncertainties. A human action model adaptation scheme is applied during run-time, and it provides a measure for modeling the human-induced uncertainties. We propose a sampling-based method to estimate human job completion time uncertainties. Next, we propose a robust task planner, which formulates the planning problem as a robust optimization problem by considering the task structure and the uncertainties. We conduct simulations of a robot arm collaborating with a human worker in an electronics assembly setting. The results show that our proposed planner can reduce task completion time when human-induced uncertainties occur compared to the baseline planner.