We have investigated the Brans-Dicke chameleon theory of gravity and obtained exact solutions of the scale factor a(t) , the scalar field (t) , an arbitrary function f () which interact with the matter Lagrangian in the action of the Brans-Dicke chameleon theory and the potential V() for different epochs of the cosmic evolution. We plot the functions a(t) , (t) , f (t) and V() for different values of the Brans-Dicke parameter. In our models, there is no accelerating solution, only a decelerating one with q > 0 . The physical cosmological distances have been investigated carefully. Further, the statefinder parameters pair and deceleration parameter are discussed.