“We’ve got £9bn of money being spent, we think, where we’re not getting value for money,” he said.
“We think we can get £2bn out of that in order to invest in our economy, invest in the most productive people in our economy, to grow the economy for the first time.”
The party says the tax band re-alignment would cost £1.2bn, and that each 1p reduction to the rate would cost £850m.
Scotland has six income tax bands, compared to three in England, Wales and Northern Ireland.
The Scottish government announced changes to income tax thresholds as part of its draft Budget earlier this month.
The thresholds for the basic and intermediate rates are both increasing, but there are no changes to the higher, advanced and top rates.
Offord said some people were “feeling fed up” with paying more in Scotland, and that those in higher bands, including some nurses and teachers, were “put upon” by shouldering the increase.