Vision-based roadside 3D object detection has attracted rising attention in autonomous driving domain, since it encompasses inherent advantages in reducing blind spots and expanding perception range. While previous work mainly focuses on accurately estimating depth or height for 2D-to-3D mapping, ignoring the position approximation error in the voxel pooling process. Inspired by this insight, we propose a novel voxel pooling strategy to reduce such error, dubbed BEVSpread. Specifically, instead of bringing the image features contained in a frustum point to a single BEV grid, BEVSpread considers each frustum point as a source and spreads the image features to the surrounding BEV grids with adaptive weights. To achieve superior propagation performance, a specific weight function is designed to dynamically control the decay speed of the weights according to distance and depth. Aided by customized CUDA parallel acceleration, BEVSpread achieves comparable inference time as the original voxel pooling. Extensive experiments on two large-scale roadside benchmarks demonstrate that, as a plug-in, BEVSpread can significantly improve the performance of existing frustum-based BEV methods by a large margin of (1.12, 5.26, 3.01) AP in vehicle, pedestrian and cyclist.