Design optimization is an important engineering design activity. Performing design optimization in the presence of uncertainty has been an active area of research. The approaches used require modeling the random variables using precise probability distributions or representing uncertain quantities as fuzzy sets. This work, however, considers problems in which the random variables are described with imprecise probability distributions, which are highly relevant when there is limited information about the distribution of a random variable. In particular, this paper formulates the imprecise probability design optimization problem and presents an approach for solving it. We present examples for illustrating the approach.