Graphene is a two dimensional material of special interest due to its unusual electronic, mechanical, chemical, optical among other properties, which suggest a wide range of applications in optoelectronics, computer, ecology, etc. The study of the optical properties of graphene is important due to its potential applications such as ultrafast photonics, optical filters, composite materials, photovoltaics and energy storage device. In this work we study the transmission and absorption properties of a quasi-regular multilayer dielectric-graphene-dielectric system. The multilayer structure is built on the quasi-regular Period-Doubling (PD) sequence. The optical response of graphene takes into account intra-band and inter-band transitions. We use the transfer-matrix method to calculate the transmission and absorption spectra. It is obtained a strong dependence on the number of layers in the system, the width of dielectric media and the optical contrast. Furthermore, we calculate the spectra for both transverse magnetic (TM) and transverse electric (TE) polarization in the infrared region.