Adsorption heat storage (AHS) is an energy-saving technology that allows low-temperature heat from renewable energy sources and various wastes to be utilized. One of the most important ways to increase the efficiency of the AHS units is to develop adsorbents with high heat storage density. This work addresses the methanol sorption on an innovative composite based on expanded vermiculite impregnated with LiCl (LiCl/Verm), which is suggested for adsorptive cycles for seasonal heat storage. Such a cycle is typical of regions with moderately cold winter, like the South of the Russian Federation as well as the Northern part of China, Europe etc. The study consists of: (1) synthesis and characterization of the composite; (2) investigation of equilibrium and dynamics of methanol sorption under operating conditions of the seasonal AHS cycle; (3) evaluation of the sorbent heat storage capacity and specific power. The heat storage capacity of LiCl/Verm under conditions of the tested cycle reaches 1.5 kJ/g. This value far exceeds that for conventional and innovative adsorbents. The specific power of 0.9 and 1.5 kW/kg can be realized during discharging and charging stages of the cycle, respectively. These findings demonstrate a high potential of the LiCl/Verm composite as methanol sorbent for AHS.