The equation of state for solid at extreme pressure and relatively low temperature is an important topic in the study of astrophysics and fundamental physics of condensed matter. Direct laser-driven quasi-isentropic compression is a powerful method to achieve such extreme states which have been developed in recent years. A lot of researches have been done in Research Center of Laser Fusion in China since 2012, which are introduced in this article. The researches include an analytical isentropic compression model, a developed characteristic method, techniques for target manufacture, and experiments performed on SHENGUANG Ⅲ prototype laser facility. The analytical isentropic compression model for condensed matter is obtained based on hydrodynamic equations and a Murnaghan-form state equation. Using the analytical model, important parameters, such as maximum shockless region width, material properties, pressure pulse profile, and pressure pulse duration can be properly allocated or chosen, which is convenient for experimental estimation and design. The characteristic method is developed based on a Murnaghan-form isentropic equation and characteristics, which can be used for experimental design, simulation, and experimental data processing. Based on the above researches, several rounds of experiments have been performed to obtain better isentropic effect by upgrading the target configurations. Five kinds of target configurations have been used up to now, which are three-step aluminum target, CH-coated planar aluminum target, CH-coated three-step aluminum target, planar aluminum target with Au blocking layer, and three-step aluminum target with Au blocking layer. The rear surface of three-step aluminum target is found to be destroyed when the loading pressure rises up to 194 GPa, and weak shock appears in CH-coated planar aluminum target and CH-coated three-step aluminum target. Besides, velocity interferometer system for any reflector (VISAR) fingers are found to decrease when the pressure rises up to about 400 GPa and disappears at 645 GPa. By reducing laser intensity, the whole interface velocities on three steps are obtained in the CH-coated three-step aluminum target and a stress-density curve is calculated. In order to eliminate the weak shock, the target configurations are upgraded by changing the ablation layer and putting a gold blocking layer after it. The experimental results show that the weak shock is eliminated and much clearer VISAR fingers are obtained when pressure rises to as high as 570 GPa.