This paper is concerned with exact model matching control (EMM) for finite Volterra series systems. First, we show a structure of a causal controller which can achieve the exact model matching to a reference model and clarify the relationship between the proposed method and the EMM for linear systems. Second, to analyse the stability of the proposed control system, we present an input dependent small gain theorem for the system with an external input, then extend it for the system with two external inputs. With the help of this theorem, we clarify the condition under which the control system is stable for the reference input magnitude within a certain range, and is also robust for small disturbances. Finally, the effectiveness of the proposed method is illustated through numerical simulations.