Neural Radiance Fields (NeRF) presented a novel way to represent scenes, allowing for high-quality 3D reconstruction from 2D images. Following its remarkable achievements, global localization within NeRF maps is an essential task for enabling a wide range of applications. Recently, Loc-NeRF demonstrated a localization approach that combines traditional Monte Carlo Localization with NeRF, showing promising results for using NeRF as an environment map. However, despite its advancements, Loc-NeRF encounters the challenge of a time-intensive ray rendering process, which can be a significant limitation in practical applications. To address this issue, we introduce Fast Loc-NeRF, which enhances efficiency and accuracy in NeRF map-based global localization. We propose a particle rejection weighting strategy that estimates the uncertainty of particles by leveraging NeRF's inherent characteristics and incorporates them into the particle weighting process to reject abnormal particles. Additionally, Fast Loc-NeRF employs a coarse-to-fine approach, matching rendered pixels and observed images across multiple resolutions from low to high. As a result, it speeds up the costly particle update process while enhancing precise localization results. Our Fast Loc-NeRF establishes new state-of-the-art localization performance on several bench-marks, demonstrating both its accuracy and efficiency. The code is available at this url.