Renewable energy generation methods such as wind power and photovoltaic power have problems of randomness, intermittency, and volatility. Gravity energy storage technology can realize the stable and controllable conversion of gravity potential energy and electric energy by lifting and lowering heavy loads. The hoisting system is an important component of a gravity energy storage system, and its lifting capacity and speed seriously restrict its energy storage capacity, energy conversion efficiency, and operational safety and reliability. In this paper, a design method for a multi-rope friction hoisting system of a vertical shaft gravity energy storage system is proposed. The parameter design and calculation of the hoisting rope, balance rope, and friction wheel of the friction hoisting system under typical conditions were carried out. The static and dynamic anti-slip capabilities of the friction hoisting system under the typical condition were explored. The results show that the maximum acceleration and deceleration speed of the compacted strand wire rope scheme is the largest, and the lifting and lowering time is the shortest. The maximum acceleration and deceleration speed of the triangular strand wire rope scheme is the lowest, and the lifting and lowering time is the longest. The dynamic tension of the hoisting rope at the heavy-load end is positively correlated with the acceleration, and the maximum value occurs in the accelerated lifting stage and decelerated lowering stage of the heavy load. The static anti-slip safety factor between the hoisting rope and the friction lining and the specific pressure between the hoisting rope and the friction lining comply with the requirements of China’s Safety Regulations for Coal Mines. The dynamic anti-slip safety factor of the hoisting system under different rope selection schemes is greater than the minimum value of 1.25 stipulated in the Safety Regulations for Metal and Nonmetal Mines. The research results are of great significance for the safety, reliability, and stable and efficient energy storage of a gravity energy storage system.