Sandal Castle’s visitor centre will only open during the summer, under cost-saving measures being drawn up by Wakefield Council.
The proposal is part of the council’s budget plan for the next year which includes a total of £38m of savings.
Council bosses originally wanted to close the centre completely to save money.
But the latest plan would see the centre will open from noon until 4pm on weekends from June to August.
Coun Les Shaw, cabinet member for culture, leisure and sport, said: “We are facing tough times with government cuts and have to make savings.
“These proposals will help to close the gap in the budget for the upcoming year.
“We’ve saved £23m in this financial year and next year we face the challenge of saving another £38m.
“Unfortunately, difficult decisions need to be made but we believe that these proposals at Sandal Castle visitor centre offer the best option for its future.”
As part of the plans, the council also hopes to host a number of events including drama productions and concerts to generate income.
People will be able to give their views at two consultation sessions at the centre.
They will be held on Thursday, February 12 from 2.30pm until 7.30pm and on Saturday, February 28 from 1pm until 3pm.