Video compression benefits from advanced chroma intra prediction methods, such as the Cross-Component Linear Model (CCLM) which uses linear models to approximate the relationship between the luma and chroma components. Recently it has been proven that advanced cross-component prediction methods based on Neural Networks (NN) can bring additional coding gains. In this paper, spatial information refinement is proposed for improving NN-based chroma intra prediction. Specifically, the performance of chroma intra prediction can be improved by refined down-sampling or by incorporating location information. Experimental results show that the two proposed methods obtain 0.31%, 2.64%, 2.02% and 0.33%, 3.00%, 2.12% BD-rate reduction on Y, Cb and Cr components, respectively, under All-Intra configuration, when implemented in Versatile Video Coding (H.266/VVC) test model. Index Terms-Chroma intra prediction, convolutional neural networks, spatial information refinement.