Despite the remarkable achievements of neural radiance fields (NeRF) in representing 3D scenes and generating novel view images, the aliasing issue, rendering 'jaggies' or 'blurry' images at varying camera distances, remains unresolved in most existing approaches. The recently proposed mip-NeRF has effectively addressed this challenge by introducing integrated positional encodings (IPE). However, it relies on MLP architecture to represent the radiance fields, missing out on the fast training speed offered by the latest grid-based methods. In this work, we present mip-Grid, a novel approach that integrates anti-aliasing techniques into grid-based representations for radiance fields, mitigating the aliasing artifacts while enjoying fast training time. Notably, the proposed method uses a single-scale shared grid representation and a single-sampling approach, which only introduces minimal additions to the model parameters and computational costs. To handle scale ambiguity, mip-Grid generates multiple grids by applying simple convolution operations over the shared grid and uses the scale-aware coordinate to retrieve the appropriate features from the generated multiple grids. To test the effectiveness, we incorporated the proposed approach into the two recent representative grid-based methods, TensoRF and K-Planes. The experimental results demonstrated that mip-Grid greatly improved the rendering performance of both methods and showed comparable performance to mip-NeRF on multi-scale datasets while achieving significantly faster training time.