A multi-attribute trajectory consists of a spatio-temporal trajectory and a set of descriptive attributes. Such data enrich the representation of traditional spatio-temporal trajectories to have comprehensive knowledge of moving objects. Range query is a fundamental operator over multi-attribute trajectories. Such a query contains two predicates, spatio-temporal and attribute, and returns the objects whose locations are within a distance threshold to the query trajectory and attributes contain expected values. There are different execution plans for answering the query. To enhance the capability of a trajectory database, an optimizer is essentially required to (i) accurately estimate the cost for alternative query strategies in terms of disk accesses, (ii) build a decision-making module that automatically sorts the data in an appropriate way and selects the optimal query plan, and (iii) update the analytical models when new trajectories are arrived. The cost model supports both uniform and non-uniform spatio-temporal data distribution and incorporates attribute distribution. The optimizer is fully developed inside a database system kernel and comprehensively evaluated in terms of accuracy and effectiveness by using large real and synthetic datasets.