Apparatus for stabilizing a rotating block of wood from which veneer is being peeled in a veneer lathe, and a method for its operation. A block stabilizer includes a massive stabilizer head having paired rollers which extend along a majority of the length of the block of wood, parallel with the axis of rotation of the block being peeled. Sensors produce electrical signals used to inform a computer of the location of the veneer knife. The computer provides position orders to move the block stabilizer head to hold the surfaces of the rollers at the expected location of the peripheral surface of the block in response to movement of the veneer knife during the entire process of peeling veneer from the block. A sensor is provided to measure the surface speed of the periphery of the block being peeled and computer control is provided to temporarily change the relationship between the location of the veneer knife and the location of the rollers, in response to sensing that the block is larger than expected in view of the location of the veneer knife.