We propose a type of reflectionless graphene perfect absorber (GPA) in which the reflection channel is forbidden, while the transmission channel is open. Peak absorption of 99.97% in the near-infrared is numerically demonstrated for monolayer graphene loaded on a one-dimensional silicon photonic crystal slab with rhomboid cross sections that supports parity symmetric unidirectional guided resonances (UGRs). Based on the proposed GPA, a transmissive optical modulator with a modulation depth of about 28 dB and an insertion loss of 0.31 dB by varying the Fermi energy level graphene from 0.3 eV to 0.7 eV is numerically presented. Remarkably, the design strategy can be straightforwardly applied to other two-dimensional (2D) materials. Our study may find promising applications in 2D material-based optical modulators and filters.