This paper describes the implementation of neutron-stimulated emission computed tomography (NSECT) for non-invasive imaging and reconstruction of a multi-element phantom. The experimental apparatus and process for acquisition of multi-spectral projection data are described along with the reconstruction algorithm and images of the two elements in the phantom. Independent tomographic reconstruction of each element of the multi-element phantom was performed successfully. This reconstruction result is the first of its kind and provides encouraging proof of concept for proposed subsequent spectroscopic tomography of biological samples using NSECT.