Computed Tomography (CT) is commonly used for cancer screening as it utilizes low radiation for the scan. One problem with low-dose scans is the noise artifacts associated with low photon count that can lead to a reduced success rate of cancer detection during radiologist assessment. The noise had to be removed to restore detail clarity. We propose a noise removal method using a new model Convolutional Neural Network (CNN). Even though the network training time is long, the result is better than other CNN models in quality score and visual observation. The proposed CNN model uses a stacked modified U-Net with a specific number of feature maps per layer to improve the image quality, observable on an average PSNR quality score improvement out of 174 images. The next best model has 0.54 points lower in the average score. The score difference is less than 1 point, but the image result is closer to the full-dose scan image. We used separate testing data to clarify that the model can handle different noise densities. Besides comparing the CNN configuration, we discuss the denoising quality of CNN compared to classical denoising in which the noise characteristics affect quality.