Chief executive Jim Brown said it was the bank's fifth consecutive quarter in profit.
Danske Bank in Northern Ireland posted a pre-tax profit of £31.5m in the first quarter of 2015.
Its UK CEO Gerry Mallon said it was a significant improvement on the same period last year.
"Our underlying financial performance has continued its upward trajectory and alongside this we are also maintaining a prudent approach to cost management," he said.
He added: "As business and consumer confidence continues to improve across the local economy, we expect demand for finance to increase further."
The Ulster Bank results are for its business across the island of Ireland, whereas the Danske Bank results are for Northern Ireland only.
While Ulster Bank reported profits, its parent company RBS posted an attributable loss of £446m in the first quarter of 2015 because of legal and restructuring costs.
RBS reported an operating profit of £325m - a figure much lower than the £1.28bn in the same period of 2014.
However, Ulster Bank's £51m operating profit was a substantial increase on the £9m posted in the first quarter of last year.
Mr Brown said: "This quarter sees sustained progress across the key areas, demonstrating the underlying strength of the core Ulster Bank franchise."
Ulster Bank has reported an operating profit of £51m for the first three months of the year.