"While expectations remain poor, we estimate that real GDP rose by 5.5 per cent during the quarter, the best performance in a year," the bank said in a note.
"There has been a modest revival in the industrial and construction sectors, finance and trade look buoyant, and public spending has been robust lately."
In the first quarter the economy had grown only 4.4 per cent, a 17-quarter low, on account of moderation in services, agriculture sectors and contraction in industrial sector. In the previous fiscal the growth slowed to a decade low of near 5 per cent.
But earlier, in the day Dun & Bradstreet pegged the second quarter growth at a much lower 4.5 per cent.
The note said second quarter GDP growth could also be a pleasant surprise to the markets because of the impact from a good monsoon and high prices to agriculture sector activity and income.
The Deutsche note said the industrial sector growth momentum improved through the September quarter, as evident from the industrial production growth trend.
The three-month average of factory output growth rose to 1.7 per cent in Q2, from -1 per cent in the April-June period, led by an across the board improvement in electricity at 8.4 per cent as against 3.5 per cent, mining at -0.1 per cent from -4.7 per cent and manufacturing production at 1.2 per cent from -1 per cent.
"Factoring in these inputs, we estimate industrial sector to rise 1.8 per cent in Q2, versus -0.9 per cent growth in the previous quarter," the note said.
The Deutsche expects the overall services sector to grow at 7 per cent in Q2, higher than 6.2 per cent in the previous quarter, while non-farm sector growth rate is seen at 5.9 per cent from 4.6 per cent last quarter.
It also expects agricultural sector growth of 2 per cent in July-September quarter, slightly lower than the 2.7 per cent in the previous quarter.
The note said that the country's fiscal deficit may not be under considerable risk of slippage as the government's fiscal strategy appears to be feasible, especially if market conditions are favourable toward disinvestment in the near- term.
It expects the rupee to be at 63 at the end of the year, but it may test 65 in the near-term on expiry of swaps.