KPMG has defined working class as having parents with "routine and manual" jobs, such as drivers, cleaners and farm workers.
It wants 29% of its partners and directors to come from working class backgrounds by 2030.
That compares with 23% of partners and 20% of directors at the moment.
KMPG said that these employees were paid 8.6% less than those from the other socio-economic groups.
In February, KMPG faced a backlash after its former chairman dismissed the notion of "unconscious bias" training.
Earlier this month the firm was accused by the Financial Reporting Council (FRC) of giving it "false and misleading" information about collapsed construction giant Carillion. In July, KPMG was also criticised by the UK accounting regulator for its "unacceptable" bank audits for the third year in a row.
According to data from the Social Mobility Commission, 39% of the UK workforce aged 16 plus are working class.
The Labour Force survey also showed that 24% were "intermediate", defined as having parents with jobs such as secretaries, call centre agents and nursery nurses. The remaining 37% had "professional backgrounds" with parents working as teachers, finance managers, software designers and accountants.
KPMG said that while its senior and junior colleagues were its most socio-economically diverse employees, working class representation in middle management grades was comparatively lower and this was contributing to the pay gaps.
The firm's diversity data is from a non-mandatory survey in which 70% of staff took part. Out of the 10,444 staff who were surveyed, 1,289 selected "I don't know" or "Prefer not to say" options when asked about their backgrounds.
The company will also train its 16,000 employees to understand the issue of socio-economic background and to recognise "invisible barriers" to progression.
Source: BBC News, Financial Times