Spectral computed tomography (SCT) generates better image quality than conventional computed tomography (CT). It has overcome several limitations for imaging atherosclerotic plaque. However, the literature evaluating the performance of SCT based on objective image assessment is very limited for the task of discriminating plaques. We developed a numerical-observer method and used it to assess performance on discrimination vulnerable-plaque features and compared the performance among multienergy CT (MECT), dual-energy CT (DECT), and conventional CT methods. Our numerical observer was designed to incorporate all spectral information and comprised two-processing stages. First, each energy-window domain was preprocessed by a set of localized channelized Hotelling observers (CHO). In this step, the spectral image in each energy bin was decorrelated using localized prewhitening and matched filtering with a set of Laguerre–Gaussian channel functions. Second, the series of the intermediate scores computed from all the CHOs were integrated by a Hotelling observer with an additional prewhitening and matched filter. The overall signal-to-noise ratio (SNR) and the area under the receiver operating characteristic curve (AUC) were obtained, yielding an overall discrimination performance metric. The performance of our new observer was evaluated for the particular binary classification task of differentiating between alternative plaque characterizations in carotid arteries. A clinically realistic model of signal variability was also included in our simulation of the discrimination tasks. The inclusion of signal variation is a key to applying the proposed observer method to spectral CT data. Hence, the task-based approaches based on the signal-known-exactly/background-known-exactly (SKE/BKE) framework and the clinical-relevant signal-known-statistically/background-known-exactly (SKS/BKE) framework were applied for analytical computation of figures of merit (FOM). Simulated data of a carotid-atherosclerosis patient were used to validate our methods. We used an extended cardiac-torso anthropomorphic digital phantom and three simulated plaque types (i.e., calcified plaque, fatty-mixed plaque, and iodine-mixed blood). The images were reconstructed using a standard filtered backprojection (FBP) algorithm for all the acquisition methods and were applied to perform two different discrimination tasks of: (1) calcified plaque versus fatty-mixed plaque and (2) calcified plaque versus iodine-mixed blood. MECT outperformed DECT and conventional CT systems for all cases of the SKE/BKE and SKS/BKE tasks (all p<0.01). On average of signal variability, MECT yielded the SNR improvements over other acquisition methods in the range of 46.8% to 65.3% (all p<0.01) for FBP-Ramp images and 53.2% to 67.7% (all p<0.01) for FBP-Hanning images for both identification tasks. This proposed numerical observer combined with our signal variability framework is promising for assessing material characterization obtained through the additional energy-dependent attenuation information of SCT. These methods can be further extended to other clinical tasks such as kidney or urinary stone identification applications.