Low-dose computed tomography (LDCT) is an important topic in the field of radiology over the past decades. LDCT reduces ionizing radiation-induced patient health risks but it also results in a low signal-to-noise ratio (SNR) and a potential compromise in the diagnostic performance. In this paper, to improve the LDCT denoising performance, we introduce the conditional denoising diffusion probabilistic model (DDPM) and show encouraging results with a high computational efficiency. Specifically, given the high sampling cost of the original DDPM model, we adapt the fast ordinary differential equation (ODE) solver for a much-improved sampling efficiency. The experiments show that the accelerated DDPM can achieve 20x speedup without compromising image quality.