For a given projection data scanned from an object, the task of optimizing CT reconstruction, tuned with different methodologies and parameters, is to produce the image with the best possible quality in terms of that the reconstructed image seems to be well balanced between apparent noises and fine image structures, or has the most visibility of pathological signals for diagnostic purpose. The former concerns the issue of general quality assessment over the whole image, as can be evaluated by a general image quality assessment (IQA) metric, e.g., SSIM, while the latter concerns the visual perception of a specific pathological signal from its background, which is task-specific and usually assessed by an observer model, e.g., Hotelling model. In the context of medical X-ray CT reconstruction, the ultimate goal is to produce the image with enough pathological information for task-specific evaluations. While considering optimizing the used reconstruction algorithm by tuning parameters, the task-specific assessment will fail in use because the task, or possible pathological signal, is unknown before the image is well reconstructed. Alternatively, in this phase only a general IQA metric can be used for optimization. In the case of the two kinds of IQA tasks are tangled in the optimization for medical X-ray CT reconstruction, it’s a very interesting problem that if the two kinds of quality assessment tasks perform consistently or inconsistently? In this paper, we develop some reference images composed by simulated lesions and computed tomography image backgrounds and four test image databases derived from reference images by adding noise. we experimentally investigate the difference of IQA among four general IQA metrics when they are used to evaluate the image quality in the database. Experimental results show that for most images, the involved IQA models give inconsistent evaluations. This discloses that there are a lot of works to do before IQA models can be used in algorithm optimization for medical X-ray CT reconstruction tasks.