In Versatile Video Coding (VVC), Cross-component Linear Model (CCLM) predicts chroma samples by assuming a linear relationship between luma and chroma components. In performing CCLM for video in YUV 4:2:0 chroma format, collocated luma samples are firstly downsampled by a low-pass filter to match luma resolution with chroma, and one linear model of luma-chroma sample pairs is applied on the reconstructed luma samples to generate the predicted chroma samples. However, the low-pass downsampling procedure ignores relative spatial variations among luma samples in proximity, such as edge and gradient information. To solve this issue, a new coding technique, namely gradient linear model (GLM), is proposed for further compression efficiency exploration beyond VVC. Instead of using a low-pass filter in CCLM, the GLM utilizes high-pass gradient filters to generate the downsampled luma values. In this paper, two GLM schemes are provided with different trade-offs between coding gain and complexity, including: 1) a 2-parameter scheme that shares the CCLM module framework but replaces the downsampling filter with high-pass gradient filters; 2) a 3-parameter scheme that further combines the luma gradients with the low-pass downsampled luma values. Based on the enhanced compression model (ECM-5.0) software from the joint video experts team (JVET), simulation results show that the 2-parameter GLM achieves average Bjɵntegaard delta-rate (BD-rate) savings of {1.01%, 1.66%, 1.81%} and {0.69%, 0.95%, 1.12%} for {Y, U, V} components under the All Intra and Random Access configurations, respectively, and the 3-parameter GLM provides {1.28%, 3.23%, 3.28%} and {0.92%, 2.19%, 2.26%} BD-rate savings for {Y, U, V} components under the All Intra and Random Access configurations, respectively. Both of the proposed GLM schemes have been adopted to the ECM software platform.