In this paper, we define the Fibonacci-Jacobsthal p-sequence and then we discuss the connection between of the Fibonacci-Jacobsthal p-sequence with the Jacobsthal and Fibonacci p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Fibonacci-Jacobsthal p-numbers by the aid of the nth power of the generating matrix of the Fibonacci-Jacobsthal p-sequence. Furthermore, we derive some properties of the Fibonacci-Jacobsthal p-sequences such as the exponential, permanental, determinantal representations and the sums by using its generating matrix.