Ex-State Sen. Dean Tran, who was convicted of fraud last year, has now admitted to covering up a sham job offer from his sister’s company.

Tran — who’s in the middle of serving an 18-month prison sentence — pleaded guilty in Boston federal court on Friday to trying to cover up the fake job offer.

Tran, 50, of Fitchburg, pleaded guilty to one count of obstruction of justice and one count of making a false statement before U.S. Senior District Court Judge Dennis Saylor IV.

Last June, Tran was indicted along with his sister, Tuyet Martin.

Tran was convicted by a federal jury last September for fraudulent collection of Pandemic Unemployment Assistance benefits and his willful omission of consulting and rental income from his tax returns in 2020, 2021 and 2022.

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“As part of an ongoing investigation into unemployment benefits and tax fraud schemes federal law enforcement interviewed Tran at his residence while executing a federal search warrant,” the Massachusetts U.S. Attorney’s office wrote. “During the interview, Tran was asked about a letter that he provided to unemployment agency officials when his benefits were briefly suspended and he was attempting to have benefits reinstated.

“Tran made material misrepresentations to the federal law enforcement agents about the letter, including that his sister and co-defendant, Tuyet Martin, had authored the letter when she was not the sole author of the letter and Tran had revised it before it was finalized and submitted to unemployment officials,” the office added.

Tran also told federal law enforcement agents that his sister’s signature appeared on the letter when in fact Tran had signed the letter — not his sister.

The charge of obstruction of justice can lead to a sentence of up to 20 years in prison, three years of supervised release, and a fine of $250,000. The charge of false statements can lead to a sentence of up to five years in prison, three years of supervised release, and a fine of $250,000.

Back in February, Tran was sentenced for scheming to defraud the Massachusetts Department of Unemployment Assistance and collecting income that he failed to report to the IRS.

He was sentenced to 18 months in prison, to be followed by two years of supervised release. Tran was also ordered to pay $25,100 in restitution to the Massachusetts Department of Unemployment Assistance and $23,327 to the IRS, as well as a $7,500 fine and a mandatory assessment of $2,300.

After Tran’s State Senate term ended in 2021, Tran fraudulently received pandemic unemployment benefits while employed as a paid consultant for a New Hampshire-based retailer of automotive parts, the Automotive Parts Company. Tran fraudulently collected $30,120 in pandemic unemployment benefits.

Tran also concealed $54,700 in consulting income that he received from the Automotive Parts Company from his 2021 federal income tax return. This was in addition to thousands of dollars in income that Tran concealed from the IRS while collecting rent from tenants who rented his Fitchburg property from 2020 to 2022.