Almost all of CuxS compounds only produce the simple two-electron transferred products CO and HCOOH but it remains a large challenge to obtain the multiple-electron transferred hydrocarbon products in electrocatalytic CO2 reduction reaction (CO2RR). Moreover, identifying the distinct contributions of S atoms to catalysis, particularly for catalytic activity and product selectivity in electrocatalytic CO2RR, remains a challenging task. Herein, we introduce a model catalyst based on a conductive two-dimensional metal-organic framework with defined Cu-S4 active sites, named Cu3(THT)2 (THT = 2,3,6,7,10,11-hexathiotriphenylene) for CO2RR. Unlike the precursor catalyst Cu3(HITP)2 with Cu-N4 motifs that predominantly produce common two-electron transferred product CO (40% selectivity), Cu3(THT)2 shifts the primary product to deep reduction product CH4. At -1.4 V versus the reversible hydrogen electrode (RHE), Cu3(THT)2 achieves a Faradaic efficiency of 63.5% for CH4 and the current density reaches a high value of -298.3 mA cm-2. Theoretical studies indicate that the electron-rich Cu-S4 sites stabilize and activate the key intermediate *CO more effectively than Cu-N4 sites. Furthermore, S atoms can accept electrons and form weak S···O interactions with *CO, providing additional stabilization for *CO. This study is the first to show that non-metallic S centers around catalytic metal sites can significantly enhance and tune product selectivity in CO2RR.