It predicts GDP will rise 0.3% this quarter. The CBI projects quarter-on-quarter growth will then stay at between 0.3% and 0.4% for the rest of 2013.
The CBI predicted 1.4% growth for 2013 in November. It is sticking with its forecast of 2% UK growth in 2014, which would still be well below a long-term average of around 2.5% per annum.
CBI director-general John Cridland said: "We are beginning to see the return of organic growth, with clear signs that firms offering the right products into the right markets are growing sales and expanding."
However, he added: "External risks to the outlook in the eurozone and further afield are likely to keep growth at home and abroad in check. The potential for eurozone tensions to flare up again, coupled with tough conditions in the domestic market, explain why business confidence remains patchy. After the uncertainties of 2012, the fear of external storm clouds lingers."
The CBI sees little change in UK unemployment, on the International Labour Organisation measure, during 2013 and 2014 and predicts levels of 2.5 million and 2.42 million respectively.