The invention relates to a device and process for converting organic waste to biogas with high methane content and improved organic conversion efficiency. Disclosed process consists of two stages and in the first stage, shredded organic waste is digested in primary digester in which biodegradable organic fractions present in waste gets converted to volatile fatty acids and alcohols dissolved in aqueous solution by hydrolytic and acidogenic microorganisms. Primary digester effluent pH, is adjusted to about 6.8-7.5 by addition of controlled alkali solution. Neutralized waste slurry is separated into liquid solution called as leachate and digested solid sludge. In the second stage, liquid leachate comprising volatile fatty acids are converted to biogas with methane content in the range 80-86% by methanogenic microbial culture in main digester under anaerobic conditions. This invention further describes optimized primary and main digester configurations with operating conditions to improve organic conversion efficiency in both the digesters.