The Labour run south east London authority says the level of its council tax has risen 27% over the last 10 years, compared to more than 80% in neighbouring Conservative-run Bexley and Bromley LBCs.
Greenwich leader Chris Roberts will be asking the full council to back the proposal when it sets its budget next month.
Mr Roberts said: “For the past 10 years Greenwich has established a record which is all but unparalleled across London for rigorous and efficient management of its budgets.
"While continuing to levy what is almost the lowest cumulative Council Tax increase in London, we have seen Greenwich go from having the second highest Council Tax in London to being 22nd of 32 boroughs.”
“At the same time, we have invested in major service and infrastructure improvements, including the development of the multi-purpose Eltham Centre, the development of 23 nurseries and the payment of£1m to fund an extra dedicated Violent and Organised Crime Unit, which has in its first six months of operation arrested several known emerging gang leaders.”