Diffusion models have emerged as a powerful method in various applications. However, their application to Short-Term Electricity Load Forecasting (STELF) -- a typical scenario in energy systems -- remains largely unexplored. Considering the nonlinear and fluctuating characteristics of the load data, effectively utilizing the powerful modeling capabilities of diffusion models to enhance STELF accuracy remains a challenge. This paper proposes a novel diffusion model with multi-frequency reconstruction for STELF, referred to as the Multi-Frequency-Reconstruction-based Diffusion (MFRD) model. The MFRD model achieves accurate load forecasting through four key steps: (1) The original data is combined with the decomposed multi-frequency modes to form a new data representation; (2) The diffusion model adds noise to the new data, effectively reducing and weakening the noise in the original data; (3) The reverse process adopts a denoising network that combines Long Short-Term Memory (LSTM) and Transformer to enhance noise removal; and (4) The inference process generates the final predictions based on the trained denoising network. To validate the effectiveness of the MFRD model, we conducted experiments on two data platforms: Australian Energy Market Operator (AEMO) and Independent System Operator of New England (ISO-NE). The experimental results show that our model consistently outperforms the compared models.