That reflects a predicted annual growth rate of 0.6%, some way short of the 3.6% achieved in the previous five years.
The market will add 122 million cases between 2014 and 2020, the IWSR said.
The highest growth will be in Asia, with China and India driving growth.
China and India currently account for 620 million and 290 million cases of spirits per year. They are the two largest spirits markets in the world.
Population growth and rising disposable income levels in many emerging markets will increase sales globally, the IWSR reported.
At its investor conference last week, Diageo predicted that rising income levels in the developing world would expand its potential consumer base by 90% in the next ten years.
The IWSR also predicts volume and value growth in mature markets such as the UK and US, however.
The fastest growing spirits categories will be whisky and tequila, it said. They will show annual growth rates of 3.8% and 2.9% respectively through 2014 to 2020.
Total annual consumption of whisky will rise to 467.4m cases, overtaking vodka to become the second-largest spirits category by the end of the decade.