The invention provides a machining center for machining a workpiece by moving a grinding wheel and the workpiece relative to each other in the X, Y and Z directions. The machining center has a main spindle for removably mounting a grinding wheel, a spindle head for rotationally supporting the main spindle, a table for mounting the workpiece, a column for movably supporting the spindle head, and tool dressing means having a dresser spindle, provided over the spindle head to move in the vertical direction toward and away from the grinding wheel mounted to the main spindle, for mounting a dresser for truing or dressing the outer peripheral surface of the grinding wheel.