The morphology of aggregates has a significant effect on the mechanical performance of aggregate-based materials such as asphalt concrete and cement concrete. This paper obtains shape indexes of aggregates, including aggregate sieve size, orientation, sphericity, and volume. The four indexes can be obtained through a virtual measurement method based on the minimum axis-aligned bounding box (AABB) of a three-dimensional (3D) solid model of aggregate. The methodology consists of three main steps: (1) the 3D solid model of each aggregate is developed from X-ray computed tomography (CT) images for aggregate cross sections, and the aggregate sphericity and volume are calculated; (2) the 3D aggregate model is rotated from the initial orientation to find a target orientation at which a minimum AABB occurs; based on that, the aggregate initial orientation is determined by the direction of the longest side of the minimum AABB and the angle rotated; and (3) the searching route for the cross section that determines the sieve size of the aggregate is computed, and the cross section with the longest length is identified to calculate the aggregate sieve size. The 3D solid models developed in this paper are very close to real aggregates, and contain intact geometric boundary information in their 3D internal structures. Laboratory measurement indicates that the virtual measurement method can significantly facilitate the accuracy, efficiency, and automation of aggregate shape characterization.