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The firm, which is part-owned by the government, recorded an operating profit of £713 million for the three-month period.
This is a substantial improvement on the £1.35 billion loss it made in the final quarter of 2009, but shares were still down in morning trading.
By 13:18 BST, its stock was priced at 45.11p on the FTSE 100 in London - a fall of 3.12p.
This is below the 50p per share the government paid to bail out RBS at the height of the financial crisis.
According to Reuters, investors are worried about the bank's exposure to the growing debt problems in the eurozone.
Chief executive officer Stephen Hester said "significant progress" has been made in restoring the bank to "standalone growth".
However, he warned "quarterly progress may not always be smooth" due to volatility in the markets and the bank's outlook.
Posted by Greg Secker
