Polarization is one of the basic properties of electromagnetic waves. Control and manipulation of polarization by devices based on metasurfaces have versatile applications in modern technologies. We propose a broadband reflective cross-polarization converter in the THz region based on an array of circular-end graphene rectangular patches. Efficient polarization conversion was accomplished through dipole graphene plasmon resonances (DGPRs), either along the long or the short axis of the graphene patches. As the width of the rectangles increased, a new longitudinal dipole mode appeared due to the circular ends of the patches. It grew strong and connected the original DGPRs, constructing an ultrabroad conversion band with efficiency over 94% from approximately 2.5 to 5.0 THz. The relative bandwidth was nearly 66%, surpassing most broadband converters reported. Such broad conversion held for a wide incident angle range as DGPRs were robust to the direction of irradiation. Due to the adjustable optical properties of graphene, the broad conversion band can be tuned. These findings are inspiring for creating broadband, compact and dynamic optoelectrical devices in the THz range.