The organic fraction of municipal solid waste (OFMSW) is recognized as a suitable substrate for the anaerobic digestion (AD) process and is currently considered a mature technology. A promising strategy to enhance biogas yield and productivity is the co-digestion of OFMSW with other organic biomass, such as green waste (GW), a mixture of leaves, grass, and woody materials originated from private yards and public greenspace management. The main limitation to the use of GW for biogas production is the high percentage of the lignocellulosic fraction, which makes necessary a pretreatment of delignification to dissolve the recalcitrant structure. In this study, a new strategy of sustainable bio-delignification using the white-rot fungi Bjerkandera adusta (BA) in comparison with other chemical pretreatments were investigated. Untreated and treated GW were, respectively, submitted to anaerobic co-digestion with OFMSW. AD processes were carried out in a lab-scale plant for 30 days in thermophilic conditions (55 °C). Biogas cumulative production was increased by about 100% in the case of treated GW compared with that of just OFMSW, from 145 to 289 Nm3 CH4/ton SV, and productivity almost doubled from 145 to 283 Nm3/ton FM * day. The measured average methane content values in the cumulative biogas were 55% from OFMSW and 54% from GW. Moreover, over 95% of the biogas was produced in 20 days, showing the potential opportunity to reduce the AD time.