This study aims to model a human-machine voice interaction process by top-down modeling methods and predict human performance and satisfaction during voice interaction. The present work provides new insights and methods for evaluating the effectiveness of different designs of voice interactive systems. Based on Queuing Network-Model Human Processor (QN-MHP) and voice interaction theories, the present research developed models to predict human voice-interaction completion time and user satisfaction under different speak recognition conditions (i.e., recognize natural language and recognize restricted language), system activation methods (i.e., wakeup, click-to-activate, hold-to-talk, and direct-talk), the average voice recognition accuracy (continuous variables), and the average voice recognition delays (continuous variables). In conclusion, based on QN-MHP, models were developed to predict human task completion time and user experiences considering different designing parameters. As an example, these models were applied in home environments to evaluate the effectiveness of different designs of the voice-interactive system for a home service robot. The models proposed by this research can provide designers and engineers with a useful tool for designing, optimizing, and applying intelligent voice-interactive systems under different requirements.