The main aim of this paper is to define and study a new confluent hypergeometric matrix function, say, (m,n)-Kummer's matrix function of two complex variables. The radius of regularity and recurrence relation on this function is established. The effect of differential operator on this function is investigated. We study the operation of a differential operator on the Hadamard product of two (m,n)-Kummer's matrix functions. Finally, we define the composite (m,n)-Kummer's matrix functions and the effect of differential operator on this function is investigated