The group said adding a tax per unit to off-licence sales would raise £1.1 billion over the next five years.
The CSJ claims 1.6 million people in the UK are addicted to alcohol in its Ambitious for Recovery report.
It wants to see money raised from the tax spent “solely on setting up a network of abstinence-based rehabilitation centres and funding sessions within them”.
CSJ director Christian Guy said: “Addiction rips into families, makes communities less safe and entrenches poverty.
“For years full recovery has been the preserve of the wealthy – closed off to the poorest people and to those with problems who need to rely on a public system. We want to break this injustice wide open.”
The CSJ said half a penny per unit should be added between 2015 and 2017, raising £155 million a year, and then wants this upped to a penny per unit between 2018 and 2020, raising £290 million per year.
It then believes this should go up to one-and-a-half pence per unit until 2023, raising £410 million per year, and then to two pence per unit from 2014, by which time the government would be raking in £520 million per year.
The Wine and Spirit Trade Association hit back, saying: “UK consumers already pay some of the highest rates of duty on alcohol in Europe. Currently, the UK has the third highest rate of duty on wine and the fourth highest duty rate for spirits in the EU.
“Further increasing the cost of wine and spirits would undermine an important UK industry which supports almost half a million jobs and in 2012/13 over £40bn of economic activity.”