This paper presents an approach for modeling user's driving-characteristics in a steering task, and determining the parameters of a virtual fixture to assist the user-control on the basis of his/her task-performances. First, we briefly introduce our assistive human-robot interaction (HRI) interface and a virtual fixture as backgrounds related to this research. The designed HRI interface provides assistance by actively constraining the user-control with a virtual fixture. Second, we discuss a way to model a user's driving-characteristics in a steering task. In modeling the driving-characteristics, we use techniques from inverse optimal control (IOC), where known basis functions (speed, steering, and proximities to inner/outer road boundary) are employed to design a cost function. Third, we describe the experimental setup and procedures to obtain user-demonstrated data from human subjects. Utilizing the obtained data sets, we infer the unknown parameter vector by solving inverse optimal control. Afterward, the user's driving-characteristics are expressed in terms of the balances of the inferred parameters, allowing us to find a relationship between the modeled driving-characteristics and task-completion time. Finally, we present a method to set a virtual fixture for a newly given task by predicting the user's task-performances.