Named after the Indian city of Kolkata (formerly Calcutta), she was constructed at Mazagon Dock Limited (MDL) and was handed over to the navy on 10 July 2014 after completing her sea trials.

The issue detected was the generation of additional noise, which occurred when the engine, gearbox and shaft were operated together, but which worked issue-free when run independently.

The issues were fixed and the sea trials were completed by February 2014, when the ship returned to MDL to undergo minor work before delivery.

[17][18][19] On 7 March 2014, during a complete check-up of the ship's machinery to fix the problems found during sea trials,[17] a naval officer was killed and several workers were injured when a valve on a CO2 bottle malfunctioned during a test of the vessel's carbon dioxide fire-fighting unit at the Mazagaon dockyard.

Kolkata's engineering officer-designate, Commander Kuntal Wadhwa, inhaled a large amount of gas and was rushed to St George's Hospital, where he was pronounced dead.

[17] As part of her pre-commissioning weapon trials at sea, Kolkata test-fired a BrahMos missile off Karwar's coast on 9 June 2014, and the test met all parameters.

About 55 nautical miles southwest of Aden, a drone or missile struck the Barbados-flagged bulk carrier MV True Confidence.

When INS Kolkata arrived on the site, it used its onboard aircraft and boats and rescued 21 crew members, including an Indian national, via life rafts.

[51][52][53] On 17 March 2024, INS Kolkata rescued 17 crew members and captured 35 pirates from the ex-Malta flagged MV Ruen, which had been hijacked on 14 December 2023, after a 40-hour long operation.

Videos of the operation released by the Navy show the pirates using the crew members as human shield as warning shots were fired from the Kolkata.