A wideband fractal rectangular dielectric resonator antenna (RDRA) based on the hook-shaped dipole is proposed for wireless communication, which exhibits stable, symmetric radiation patterns and low cross-polarization. The antenna consists of a Koch-like fractal rectangular dielectric resonator antenna (FRDRA) and a hook-shaped electric dipole (HSE-Dipole), which are equivalent to the magnetoelectric (ME) dipoles. The symmetrical radiation pattern with gain enhancement and suppression of backward lobe is achieved by the complementary combination of the electric and magnetic dipoles. The Koch-like fractal structure is used to improve the impedance matching of the RDRA with 15% size reduction. The antenna is excited by the substrate integrated waveguide (SIW) feeding network, which takes the advantage of compact size and low insertion loss. Due to the air gap between the FRDRA and HSE-Dipole, the fundamental TE1δ1 and high-order TE1δ2 modes of the RDRA are both generated to obtain the 19.5% impedance bandwidth. The prototype is fabricated and measured to validate the antenna design, which shows remarkable radiation performance including the front to back ratio (FTBR) of >20 dB, the average gain of 5.96 dBi and low cross-polarization.