We define the complex-type Narayana sequence and give miscellaneous properties of this sequence by using the matrix method. Also, we study the complex-type Narayana sequence modulo m . In addition, we describe the complex-type Narayana sequence in a 3generator group and investigate the sequence in finite groups in detail. Finally, we give the lengths of the periods of the complex-type Narayana sequences in polyhedral groups (n, 2, 2), (2, n, 2) and (2, 2, n) with respect to the generating triple ( x, y, z) as application of the results produced.