In this paper, we define the Hadamard-type Padovan-p sequence by using the Hadamard-type product of characteristic polynomials of the Padovan sequence and the Padovan-p sequence. Also, we derive the generating matrices for these sequences. Then using the roots of characteristic polynomial of the Hadamard-type Padovan-p sequence, we produce the Binet formula for the Hadamard-type Padovan-p numbers. Also, we give the permanental, determinantal, combinatorial, exponential representations and the sums of the Hadamard-type Padovan-p numbers.