Despite the indispensable role of X-ray computed tomography (CT) in diagnostic medicine field, the associated ionizing radiation is still a major concern considering that it may cause genetic and cancerous diseases. Decreasing the exposure can reduce the dose and hence the radiation-related risk, but will also induce higher quantum noise. Supervised deep learning can be used to train a neural network to denoise the low-dose CT (LDCT). However, its success requires massive pixel-wise paired LDCT and normal-dose CT (NDCT) images, which are rarely available in real practice. To alleviate this problem, in this paper, a shift-invariant property based neural network was devised to learn the inherent pixel correlations and also the noise distribution by only using the LDCT images, shaping into our probabilistic self-learning framework. Experimental results demonstrated that the proposed method outperformed the competitors, producing an enhanced LDCT image that has similar image style as the routine NDCT which is highly-preferable in clinic practice.