BP said its profits had fallen by 51% to $5.9bn (£4.1bn), compared with $12.1bn in 2014.
Underlying fourth-quarter profits fell to $196m, compared with $2.2bn for the same period in the previous year.
Last year, it said 4,000 jobs would go in its upstream division as part of a $2.5bn restructuring programme.
BP said its upstream business, which covers exploration and production, slumped to a $728m loss in the final quarter.
The latest reduction of up to 3,000 jobs by the end of 2017 affects staff and contractors in its downstream segment.
This refers to its refined oil products, such as fuel, lubricants and petrochemicals, for making products such as paint and plastic bottles.
The oil giant was the biggest faller on the FTSE 100 index, tumbling 8.1% by mid-morning.