This paper presents an intra line copy mode, which introduces a finer-granularity block partitioning structure for the intra copying technique, to further improve the coding efficiency for screen content. This mode first divides a prediction block horizontally or vertically into 1-pixel-wide lines and then operates intra copying line-by-line from the reconstructed pixels in the current frame. It shares some parallels with the notion of string matching widely used for lossless data compression. It, however, is more compliant to the current HEVC design and is parallel-friendly. This paper shall detail its various design issues, including the design of a fast algorithm based on hashing techniques and the impact of search window size on its performance and complexity trade-off. Experimental results show that the proposed mode can offer 2.7-12.9% of BD-rate reductions, with 26% increase of encoding runtime while keeping the decoding runtime unchanged, when integrated into the SCM-1.0 test model.