A new Plus-shaped Dielectric Resonator Antenna (DRA) with parasitic rectangular elements (P-DRA) is proposed for multi-band applications. The antenna is made up of a plus-shaped dielectric resonator and four parasitic rectangular elements that create a rectangular antenna with four L-slots. The P-DRA has a relative permittivity of 15 and is mounted on a 50-ohm microstrip feeding line with a partial and defective ground structure. The proposed R-DRA is designed with the dimensions (15 x 12 x 6.4) mm3. The impedance bandwidth, radiation pattern, return loss, and antenna gain are obtained using an electromagnetic simulator that employs the finite element method. Furthermore, the obtained results are validated by another 3D simulator using the finite integration technique solver. The P-DRA is designed for multiband applications such as sub-7 GHz (4-8 GHz), wireless local area network (WLAN), X-band (9-10) GHz, and (11-12) GHz, and Ku-band (13-16) GHz. The parasitic elements not only contribute to the excitation of additional frequency bands but also enhance the bandwidth of the operating frequencies, providing two broad bands of (4-8) GHz and (13-16) GHz with integrated resonant frequencies.