In human-AI coordination scenarios, human agents usually exhibit asymmetric behaviors that are significantly sparse and unpredictable compared to those of AI agents. These characteristics introduce two primary challenges to human-AI coordination: the effectiveness of obtaining sparse rewards and the efficiency of training the AI agents. To tackle these challenges, we propose an Intrinsic Reward-enhanced Context-aware (IReCa) reinforcement learning (RL) algorithm, which leverages intrinsic rewards to facilitate the acquisition of sparse rewards and utilizes environmental context to enhance training efficiency. Our IReCa RL algorithm introduces three unique features: (i) it encourages the exploration of sparse rewards by incorporating intrinsic rewards that supplement traditional extrinsic rewards from the environment; (ii) it improves the acquisition of sparse rewards by prioritizing the corresponding sparse state-action pairs; and (iii) it enhances the training efficiency by optimizing the exploration and exploitation through innovative context-aware weights of extrinsic and intrinsic rewards. Extensive simulations executed in the Overcooked layouts demonstrate that our IReCa RL algorithm can increase the accumulated rewards by approximately 20% and reduce the epochs required for convergence by approximately 67% compared to state-of-the-art baselines.