Convolutional neural network (CNN) is now the most promising denoising methods for low-dose computed tomography (CT) images. The goal of denoising is to restore original details as well as to reduce noise, and the performance is largely determined by the loss function of the CNN. In this work, we investigate the denoising performance of CNN for three different loss functions in low dose CT images: mean squared error (MSE), perception loss using the pretrained VGG network (VGG loss), and the weighted summation of MSE and VGG losses (VGGMSE loss). CNNs are trained to map the quarter dose CT images to normal dose CT images in a supervised fashion. The image quality of denoised images is evaluated by normalized root mean squared error (NRMSE), structural similarity index (SSIM), mean and standard deviation (SD) of HU values, and the task SNR of non-prewhitening eye filter observer model (NPWE). Our results show that the CNN trained with MSE loss achieves the best performance in NRMSE and SSIM despite significant image blurs. On the other hand, the CNN trained with VGG loss reports the best score in the SD with well-preserved details but has the worst accuracy in the mean HU value. CNN trained with VGGMSE loss shows the best performance in terms of tSNR and the mean HU value and consistently high performance in other metrics. In conclusion, VGGMSE loss can subside the drawbacks of MSE or VGG loss, thus much more effective than them for CT denoising tasks.