A unimodal hazard rate function is suggested to model a failure rate that has a relatively high rate of failure in the middle of expected life time. This unimodal hazard rate function has two shape parameters. One of the parameters indicates the location (time) of the mode and the other controls the height of the mode. In effect, these two parameters index the class of unimodal hazard rate functions. The reliability function and the failure density function of the unimodal hazard rate function are relatively uncomplicated and mathematically tractable. The properties of the unimodal hazard rate function and the failure density function are investigated. The maximum likelihood method is used for the inference concerning the two parameters and an example based on real data is presented. This unimodal hazard rate function is particularly useful when the time of the peak failure rate is of prime interest. The failure distribution provides a practical way of estimating the peak failure time.