There is growing interest in the use of deep neural network (DNN) based image denoising to reduce patient’s X-ray dosage in medical computed tomography (CT). An effective denoiser must remove noise while maintaining the texture and detail. Commonly used mean squared error (MSE) loss functions in the DNN training weight errors due to bias and variance equally. However, the error due to bias is often more egregious since it results in loss of image texture and detail. In this paper, we present a novel approach to designing a loss function that penalizes variance and bias differently. Our proposed bias-reducing loss function allows us to train a DNN denoiser so that the amount of texture and detail retained can be controlled through a user adjustable parameter. Our experiments verify that the proposed loss function enhances the texture and detail in denoised images with only a slight increase in the MSE.