The weak signal strength of Raman imaging leads to long imaging times. To increase the speed of Raman imaging, line scanning and compressed Raman imaging methods have been proposed. Here we combine both line scanning and compressed sensing to further increase the speed. However, the direct combination leads to poor reconstruction results due to the missed coverage of the sample. To avoid this issue, "full-coverage" Compressed Line-scan Raman Imaging (FC-CLRI) is proposed, where line positions are random but constrained to measure each line position of the sample at least once. In proof-of-concept studies of polymer beads and yeast cells, FC-CLRI achieved reasonable image quality while making only 20-40% of the measurements of a fully-sampled line-scan image, achieving 640 μm2 FOV imaging in <2 min with 1.5 mW μm-2 laser power. Furthermore, we critically evaluate the CLRI method through comparison with simple downsampling, and have found that FC-CLRI preserves spatial resolution better while naïve downsampling provides an overall higher image quality for complex samples.