This paper discusses regression analysis of interval-censored failure time data, which occur in many fields including demographical, epidemiological, financial, medical, and sociological studies. For the problem, we focus on the situation where the survival time of interest can be described by the additive hazards model and a multiple imputation approach is presented for inference. A major advantage of the approach is its simplicity and it can be easily implemented by using the existing software packages for right-censored failure time data. Extensive simulation studies are conducted which indicate that the approach performs well for practical situations and is comparable to the existing methods. The methodology is applied to a set of interval-censored failure time data arising from an AIDS clinical trial.