Accurate weather forecasting is critical for science and society. However, existing methods have not achieved the combination of high accuracy, low uncertainty, and high computational efficiency simultaneously. On one hand, traditional numerical weather prediction (NWP) models are computationally intensive because of their complexity. On the other hand, most machine learning-based weather prediction (MLWP) approaches offer efficiency and accuracy but remain deterministic, lacking the ability to capture forecast uncertainty. To tackle these challenges, we propose a conditional diffusion model, CoDiCast, to generate global weather prediction, integrating accuracy and uncertainty quantification at a modest computational cost. The key idea behind the prediction task is to generate realistic weather scenarios at a future time point, conditioned on observations from the recent past. Due to the probabilistic nature of diffusion models, they can be properly applied to capture the uncertainty of weather predictions. Therefore, we accomplish uncertainty quantifications by repeatedly sampling from stochastic Gaussian noise for each initial weather state and running the denoising process multiple times. Experimental results demonstrate that CoDiCast outperforms several existing MLWP methods in accuracy, and is faster than NWP models in inference speed. Our model can generate 6-day global weather forecasts, at 6-hour steps and 5.625-degree latitude-longitude resolutions, for over 5 variables, in about 12 minutes on a commodity A100 GPU machine with 80GB memory. The source code is available at https://github.com/JimengShi/CoDiCast.