A roaster structure with a cover supporting member for achieving secure angular positions includes a roaster body and a ceramic cover in addition to the cover supporting member for achieving secure angular positions. The cover supporting member for achieving secure angular positions includes: a lower supporting member fixedly provided on one side of the roaster body and having a first joining end and at least one limiting groove; an upper supporting member pivotally joined to the lower supporting member and having a second joining end; at least one position-limiting member fixed on the upper supporting member and slidably inserted into the at least one limiting groove; and an extensible and retractable bar joined between the two joining ends. The ceramic cover can be lifted open and closed with respect to the roaster body and secured at any angular position via the cover supporting member for achieving secure angular positions.