A third person has been charged with murder over the death of an Indian man in southern New South Wales last month.

Ranjodh Singh's body was found on the side of the road in Willbriggie, near Griffith in late December. It was badly burnt.

Yesterday, a man and woman, were arrested at San Souci in Sydney's south and charged with murder.

Gurpreet Singh, 23, and his 20-year-old wife Harpreet Bhullar faced Sutherland Local Court separately today.

Gurpreet Singh seemed calm as he sat in the dock, but his wife was visibly upset.

The couple did not apply for bail and will remain behind bars until their next court appearance next month.

Their lawyer requested a Punjabi interpreter.

The third person, a 25-year-old man, was arrested in Wagga Wagga this morning.

Wagga Local Court heard this afternoon that Harpreet Singh will make a bail application next week.

Police have so far not commented on the motive for the killing, but they say it was not racially motivated.

At the time of his death, Ranjodh Singh was harvesting pumpkins in Griffith. He had been in Australia for a year.